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Nenad Trinajstic - One of the best experts on this subject based on the ideXlab platform.
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comparison between the wiener Index and the zagreb indices and the eccentric Connectivity Index for trees
Discrete Applied Mathematics, 2014Co-Authors: Kinkar Chandra Das, Hanul Jeon, Nenad TrinajsticAbstract:Abstract Molecular descriptors play an important role in mathematical chemistry, especially in the QSPR and QSAR modeling. Among them, a special place is reserved for the so called topological indices. Nowadays, there exists a legion of topological indices that found applications in various areas of chemistry Todeschini and Consonni (2000, 2009). Recently, we carried out comparison between several topological indices for various classes of graphs and trees (Das et al., 2012; Das and Trinajsti, 2010, 2011, 2012; Horoldagva and Das, 2012; Hua and Das, 2013). In this report, we compare the Wiener Index and the Zagreb indices and the eccentric Connectivity Index for trees.
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relationship between the eccentric Connectivity Index and zagreb indices
Computers & Mathematics With Applications, 2011Co-Authors: Kinkar Chandra Das, Nenad TrinajsticAbstract:Abstract For a (molecular) graph, the first Zagreb Index M 1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb Index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V ( G ) , then the eccentric Connectivity Index of G , ξ C ( G ) , is defined as, ∑ v i ∈ V ( G ) d i e i , where d i is the degree of a vertex v i and e i is its eccentricity. In this report we compare the eccentric Connectivity Index ( ξ C ) and the Zagreb indices ( M 1 and M 2 ) for chemical trees. Moreover, we compare the eccentric Connectivity Index ( ξ C ) and the first Zagreb Index ( M 1 ) for molecular graphs.
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on the general sum Connectivity Index of trees
Applied Mathematics Letters, 2011Co-Authors: Bo Zhou, Nenad TrinajsticAbstract:Abstract The general sum-Connectivity Index of a graph G is defined as χ α ( G ) = ∑ u v ∈ E ( G ) ( d u + d v ) α , where d u denotes the degree of vertex u in G , E ( G ) denotes the edge set of G , and α is a real number. We determine the maximum value for the general sum-Connectivity indices of n -vertex trees and the corresponding extremal trees for α α 0 , where α 0 = − 4.3586 … is the unique root of the equation 4 α − 5 α 5 α − 6 α = 3 .
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on the sum Connectivity Index
Filomat, 2011Co-Authors: Shilin Wang, Nenad TrinajsticAbstract:The sum-Connectivity Index of a simple graph G is deflned in mathematical chemistry as R + (G) = X uv2E(G) (du + dv) i 1=2
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comparison between first geometric arithmetic Index and atom bond Connectivity Index
Chemical Physics Letters, 2010Co-Authors: Kinkar Ch Das, Nenad TrinajsticAbstract:Abstract The first geometric–arithmetic Index ( GA ) [1] and atom-bond Connectivity Index ( ABC ) [2] that are recently introduced, are found to be useful tools in QSPR and QSAR studies. In this letter we compare the GA and ABC indices for chemical trees and molecular graphs. Moreover, we also compare these two indices for general graphs.
Bo Zhou - One of the best experts on this subject based on the ideXlab platform.
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on the general sum Connectivity Index of trees
Applied Mathematics Letters, 2011Co-Authors: Bo Zhou, Nenad TrinajsticAbstract:Abstract The general sum-Connectivity Index of a graph G is defined as χ α ( G ) = ∑ u v ∈ E ( G ) ( d u + d v ) α , where d u denotes the degree of vertex u in G , E ( G ) denotes the edge set of G , and α is a real number. We determine the maximum value for the general sum-Connectivity indices of n -vertex trees and the corresponding extremal trees for α α 0 , where α 0 = − 4.3586 … is the unique root of the equation 4 α − 5 α 5 α − 6 α = 3 .
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on atom bond Connectivity Index
Zeitschrift für Naturforschung A, 2011Co-Authors: Bo Zhou, Rundan XingAbstract:The atom-bond Connectivity (ABC) Index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randic Connectivity indices, and the first Zagreb Index. We determine the unique tree with the maximum ABC Index among trees with given numbers of vertices and pendant vertices, and the n-vertex trees with the maximum, and the second, the third, and the fourth maximum ABC indices for n ≥ 6.
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ON ECCENTRIC Connectivity Index
arXiv: Combinatorics, 2010Co-Authors: Bo ZhouAbstract:The eccentric Connectivity Index, proposed by Sharma, Goswami and Madan, has been employed successfully for the development of numerous mathematical models for the prediction of biological activities of diverse nature. We now report mathematical properties of the eccentric Connectivity Index. We establish various lower and upper bounds for the eccentric Connectivity Index in terms of other graph invariants including the number of vertices, the number of edges, the degree distance and the first Zagreb Index. We determine the n-vertex trees of diameter , d 3 th the minimum eccentric Connectivity Index,
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minimum general sum Connectivity Index of unicyclic graphs
Journal of Mathematical Chemistry, 2010Co-Authors: Bo Zhou, Nenad TrinajsticAbstract:The general sum-Connectivity Index of a graph G is defined as χ α (G) = ∑edges (d u + d v ) α , where d u denotes the degree of vertex u in G and α is a real number. In this report, we determine the minimum and the second minimum values of the general sum-Connectivity indices of n-vertex unicyclic graphs for non-zero α ≥ −1, and characterize the corresponding extremal graphs.
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sum Connectivity Index of molecular trees
Journal of Mathematical Chemistry, 2010Co-Authors: Rundan Xing, Bo Zhou, Nenad TrinajsticAbstract:We report lower and upper bounds for the sum-Connectivity indices of molecular trees with fixed numbers of vertices and pendant vertices.
Mohammad Reza Farahani - One of the best experts on this subject based on the ideXlab platform.
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Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7
Advances in Materials Science and Engineering, 2019Co-Authors: Fei Deng, Xiujun Zhang, Mehdi Alaeiyan, Abid Mehboob, Mohammad Reza FarahaniAbstract:In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond Connectivity Index, fourth atom-bond Connectivity Index, Randic Connectivity Index, sum-Connectivity Index, first Zagreb Index, second Zagreb Index, augmented Zagreb Index, modified Zagreb Index, hyper Zagreb Index, geometric-arithmetic Index, fifth geometric-arithmetic Index, Sanskruti Index, forgotten Index, and harmonic Index of pent-heptagonal nanosheet have been derived.
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on the atom bond Connectivity Index of titania nanotubes tio2 m n
Iraqi journal of science, 2018Co-Authors: Mohammad Reza Farahani, M Rezaei, Muhammad Jamil, Hafiz Mutee Ur Rehman, Muhammad ImranAbstract:Let G(V,E) be a simple molecular graph, for a graph G(V,E) with vertex(atom) set V and the edge(bond) set E, the third version of atom bond Connectivity Index is defined as where m v is the number of edges of G lying near to u than to v. In this research paper, we compute the third version of atomic-bond Connectivity Index of the Titania Nanotubes TiO 2 (m,n) .
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about the randic Connectivity modify randic Connectivity and sum Connectivity indices of titania nanotubes tio2 m n
Acta Chimica Slovenica, 2017Co-Authors: Wei Gao, Mohammad Reza Farahani, Muhammad ImranAbstract:The Randic Connectivity Index R(G) is one of the oldest Connectivity Index, introduced by Randic in 1975. Another Connectivity indices is the Sum-Connectivity Index X(G) introduced in 2008 by Zhou and Trinajstic. Recently in 2011, a modification of the Randic Connectivity Index of a graph G was introduced by Dvorak et al. In this paper, we compute these Connectivity topological indices for a family of molecular graphs known as titania nanotubes TiO 2 ( m,n ).
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the eccentricity version of atom bond Connectivity Index of linear polycene parallelogram benzenoid abc5 p n n
Acta Chimica Slovenica, 2016Co-Authors: Wei Gao, Mohammad Reza Farahani, Muhammad JamilAbstract:Among topological descriptors, Connectivity indices are very important and they have a prominent role in chemistry. The atom-bond Connectivity Index of a connected graph G is defined as ABC(G) = ∑(uv ∈E (G)) √((du + dv - 2)/dudv), where dv denotes the degree of vertex v of G and the eccentric Connectivity Index of the molecular graph G is defined as ξ(G) = ∑(v ∈V) dv × e(v), where e(v) is the largest distance between v and any other vertex u of G. Also, the eccentric atom-bond Connectivity Index of a connected graph G is equal to ABC5(G) =∑(uv ∈E (G)) √((e(u) + e(v) - 2)/(e(u)e(v))). In this present paper, we compute this new Eccentric Connectivity Index for an infinite family of Linear Polycene Parallelogram Benzenoid.
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computing the reverse eccentric Connectivity Index for certain family of nanocone and fullerene structures
Journal of Nanotechnology, 2016Co-Authors: Wei Gao, Mohammad Reza FarahaniAbstract:A large number of previous works reveal that there exist strong connections between the chemical characteristics of chemical compounds and drugs (e.g., melting point and boiling point) and their topological structures. Chemical indices introduced on these molecular topological structures can help chemists and material and medical scientists to grasp its chemical reactivity, biological activity, and physical features better. Hence, the study of the topological indices on the material structure can make up the defect of experiments and provide the theoretical evidence in material engineering. In this paper, we determine the reverse eccentric Connectivity Index of one family of pentagonal carbon nanocones and three infinite families of fullerenes , , and based on graph analysis and computation derivation, and these results can offer the theoretical basis for material properties.
Kinkar Ch Das - One of the best experts on this subject based on the ideXlab platform.
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comparison between the szeged Index and the eccentric Connectivity Index
Discrete Applied Mathematics, 2015Co-Authors: Kinkar Ch Das, M J NadjafiaraniAbstract:Let S z ( G ) and ? c ( G ) be the Szeged Index and the eccentric Connectivity Index of a graph G , respectively. In this paper we obtain a lower bound on S z ( T ) - ? c ( T ) by double counting on some matrix and characterize the extremal graphs. From this result we compare the Szeged Index and the eccentricity Connectivity Index of trees. For bipartite graphs we also compare the Szeged Index and the eccentricity Connectivity Index. Moreover, we show that S z ( G ) - ? c ( G ) ? - 4 for bipartite graphs and this result is not true in the general case. Finally, we classify the bipartite graphs G in which S z ( G ) - ? c ( G ) ? { - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 } .
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the relationship between the eccentric Connectivity Index and zagreb indices
Discrete Applied Mathematics, 2013Co-Authors: Hongbo Hua, Kinkar Ch DasAbstract:Let G be a simple connected graph with vertex set V(G) and edge set E(G). The first Zagreb Index M"1(G) and the second Zagreb Index M"2(G) are defined as follows: M"1(G)=@?v@?V(G)(d"G(v))^2, and M"2(G)=@?uv@?E(G)d"G(u)d"G(v), where d"G(v) is the degree of vertex v in G. The eccentric Connectivity Index of a graph G, denoted by @x^c(G), is defined as @x^c(G)=@?v@?V(G)d"G(v)ec"G(v), where ec"G(v) is the eccentricity of v in G. Recently, Das and Trinajstic (2011) [11] compared the eccentric Connectivity Index and Zagreb indices for chemical trees and molecular graphs. However, the comparison between the eccentric Connectivity Index and Zagreb indices, in the case of general trees and general graphs, is very hard and remains unsolved till now. In this paper, we compare the eccentric Connectivity Index and Zagreb indices for some graph families. We first give some sufficient conditions for a graph G satisfying @x^c(G)@?M"i(G), i=1,2. Then we introduce two classes of composite graphs, each of which has larger eccentric Connectivity Index than the first Zagreb Index, if the original graph has larger eccentric Connectivity Index than the first Zagreb Index. As a consequence, we can construct infinite classes of graphs having larger eccentric Connectivity Index than the first Zagreb Index.
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on atom bond Connectivity Index
Chemical Physics Letters, 2011Co-Authors: Kinkar Ch Das, Ivan Gutman, Boris FurtulaAbstract:The atom-bond Connectivity Index (ABC) is a vertex-degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V,E) be a graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC = ∑ ij2E √ (di + dj 2)/(di dj). Upper bounds and Nordhaus-Gaddum type results for ABC are established.
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comparison between first geometric arithmetic Index and atom bond Connectivity Index
Chemical Physics Letters, 2010Co-Authors: Kinkar Ch Das, Nenad TrinajsticAbstract:Abstract The first geometric–arithmetic Index ( GA ) [1] and atom-bond Connectivity Index ( ABC ) [2] that are recently introduced, are found to be useful tools in QSPR and QSAR studies. In this letter we compare the GA and ABC indices for chemical trees and molecular graphs. Moreover, we also compare these two indices for general graphs.
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atom bond Connectivity Index of graphs
Discrete Applied Mathematics, 2010Co-Authors: Kinkar Ch DasAbstract:The recently introduced atom-bond Connectivity (ABC) Index has been applied up until now to study the stability of alkanes and the strain energy of cycloalkanes. Furtula et al. (2009) [3] obtained extremal ABC values for chemical trees, and also, it has been shown that the star K"1","n"-"1, has the maximal ABC value of trees. In this paper, we present the lower and upper bounds on ABC Index of graphs and trees, and characterize graphs for which these bounds are best possible.
Wei Gao - One of the best experts on this subject based on the ideXlab platform.
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on the minimal general sum Connectivity Index of connected graphs without pendant vertices
IEEE Access, 2019Co-Authors: Akbar Ali, Wei Gao, Shahzad Ahmed, Muhammad Aslam MalikAbstract:The general sum-Connectivity Index of a graph $G$ , denoted by $\chi _{_\alpha }(G)$ , is defined as $\sum _{uv\in E(G)}(d(u)+d(v))^{\alpha }$ , where $uv$ is the edge connecting the vertices $u,v\in V(G)$ , $d(w)$ denotes the degree of a vertex $w\in V(G)$ , and $\alpha $ is a non-zero real number. For $\alpha =-1/2$ and $n\geq 11$ , Wang et al. [On the sum-Connectivity Index, Filomat 25 (2011) 29–42] proved that $K_{2} + \overline {K}_{n-2}$ is the unique graph with minimum $\chi _{_\alpha }$ value among all the $n$ –vertex graphs having minimum degree at least 2, where $K_{2} + \overline {K}_{n-2}$ is the join of the 2-vertex complete graph $K_{2}$ and the edgeless graph $\overline {K}_{n-2}$ on $n-2$ vertices. Tomescu [2-connected graphs with minimum general sum-Connectivity Index, Discrete Appl. Math. 178 (2014) 135–141] proved that the result of Wang et al. holds also for $n\geq 3$ and $-1\leq \alpha . In this paper, it is shown that the aforementioned result of Wang et al. remains valid if the graphs under consideration are connected, $n\geq 6$ and $-1\leq \alpha , where $\alpha _{0}\approx -0.68119$ is the unique real root of the equation $\chi _{_\alpha }(K_{2} + \overline {K}_{4}) - \chi _{_\alpha }(C_{6})=0$ , and $C_{6}$ is the cycle on 6 vertices.
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the first multiplication atom bond Connectivity Index of molecular structures in drugs
Journal of The Saudi Pharmaceutical Society, 2017Co-Authors: Wei Gao, Weifan Wang, Yiqiao Wang, Li ShiAbstract:In the field of medicine, there are a large number of new drugs synthesis every year. Before entering the clinical stage, it needs a lot of work on drug testing of the various properties. Due to the lack of a large number of laboratory technician, laboratory equipment and reagents, the drug testing of many biochemical properties are not completed. Theoretical medicine provides a theoretical way for medical researchers to obtain the pharmaceutical properties of compounds by calculation tricks. In this paper, the first multiplication atom-bond Connectivity Index of several common drugs structure are studied, and the accurate expressions are determined. These theoretical conclusions provide practical guiding significance for pharmaceutical engineering.
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about the randic Connectivity modify randic Connectivity and sum Connectivity indices of titania nanotubes tio2 m n
Acta Chimica Slovenica, 2017Co-Authors: Wei Gao, Mohammad Reza Farahani, Muhammad ImranAbstract:The Randic Connectivity Index R(G) is one of the oldest Connectivity Index, introduced by Randic in 1975. Another Connectivity indices is the Sum-Connectivity Index X(G) introduced in 2008 by Zhou and Trinajstic. Recently in 2011, a modification of the Randic Connectivity Index of a graph G was introduced by Dvorak et al. In this paper, we compute these Connectivity topological indices for a family of molecular graphs known as titania nanotubes TiO 2 ( m,n ).
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the eccentricity version of atom bond Connectivity Index of linear polycene parallelogram benzenoid abc5 p n n
Acta Chimica Slovenica, 2016Co-Authors: Wei Gao, Mohammad Reza Farahani, Muhammad JamilAbstract:Among topological descriptors, Connectivity indices are very important and they have a prominent role in chemistry. The atom-bond Connectivity Index of a connected graph G is defined as ABC(G) = ∑(uv ∈E (G)) √((du + dv - 2)/dudv), where dv denotes the degree of vertex v of G and the eccentric Connectivity Index of the molecular graph G is defined as ξ(G) = ∑(v ∈V) dv × e(v), where e(v) is the largest distance between v and any other vertex u of G. Also, the eccentric atom-bond Connectivity Index of a connected graph G is equal to ABC5(G) =∑(uv ∈E (G)) √((e(u) + e(v) - 2)/(e(u)e(v))). In this present paper, we compute this new Eccentric Connectivity Index for an infinite family of Linear Polycene Parallelogram Benzenoid.
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computing the reverse eccentric Connectivity Index for certain family of nanocone and fullerene structures
Journal of Nanotechnology, 2016Co-Authors: Wei Gao, Mohammad Reza FarahaniAbstract:A large number of previous works reveal that there exist strong connections between the chemical characteristics of chemical compounds and drugs (e.g., melting point and boiling point) and their topological structures. Chemical indices introduced on these molecular topological structures can help chemists and material and medical scientists to grasp its chemical reactivity, biological activity, and physical features better. Hence, the study of the topological indices on the material structure can make up the defect of experiments and provide the theoretical evidence in material engineering. In this paper, we determine the reverse eccentric Connectivity Index of one family of pentagonal carbon nanocones and three infinite families of fullerenes , , and based on graph analysis and computation derivation, and these results can offer the theoretical basis for material properties.