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Bo Zhou  One of the best experts on this subject based on the ideXlab platform.

On the distance α Spectral Radius of a connected graph
Journal of Inequalities and Applications, 2020CoAuthors: Haiyan Guo, Bo ZhouAbstract:For a connected graph G and $\alpha \in [0,1)$, the distance αSpectral Radius of G is the Spectral Radius of the matrix $D_{\alpha }(G)$ defined as $D_{\alpha }(G)=\alpha T(G)+(1\alpha )D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of G and $D(G)$ is the distance matrix of G. We give bounds for the distance αSpectral Radius, especially for graphs that are not transmission regular, propose local graft transformations that decrease or increase the distance αSpectral Radius, and determine the graphs that minimize and maximize the distance αSpectral Radius among several families of graphs.

The αSpectral Radius of general hypergraphs
Applied Mathematics and Computation, 2020CoAuthors: Hongying Lin, Bo ZhouAbstract:Abstract Given a hypergraph H of order n with rank k ≥ 2, denote by D ( H ) and A ( H ) the degree diagonal tensor and the adjacency tensor of H, respectively, of order k and dimension n. For real number α with 0 ≤ α α D ( H ) + ( 1 − α ) A ( H ) . First, we establish a upper bound on the αSpectral Radius of connected irregular hypergraphs. Then we propose three local transformations of hypergraphs that increase the αSpectral Radius. We also identify the unique hypertree with the largest αSpectral Radius and the unique hypergraph with the largest αSpectral Radius among hypergraphs of given number of pendent edges, and discuss the unique hypertrees with the next largest αSpectral Radius and the unicyclic hypergraphs with the largest αSpectral Radius.

On adjacencydistance Spectral Radius and spread of graphs
Applied Mathematics and Computation, 2020CoAuthors: Haiyan Guo, Bo ZhouAbstract:Abstract Let G be a connected graph. The greatest eigenvalue and the spread of the sum of the adjacency matrix and the distance matrix of G are called the adjacencydistance Spectral Radius and the adjacencydistance spread of G, respectively. Both quantities are used as molecular descriptors in chemoinformatics. We establish some properties for the adjacencydistance Spectral Radius and the adjacencydistance spread by proposing local grafting operations such that the adjacencydistance Spectral Radius is decreased or increased. Hence, we characterize those graphs that uniquely minimize and maximize the adjacencydistance Spectral radii in several sets of graphs, and determine trees with small adjacencydistance spreads. It transpires that the adjacencydistance Spectral Radius satisfies the requirements of a branching index.

On the αSpectral Radius of graphs
Applicable Analysis and Discrete Mathematics, 2020CoAuthors: Haiyan Guo, Bo ZhouAbstract:For 0 ? ? ? 1, Nikiforov proposed to study the Spectral properties of the family of matrices A?(G) = ?D(G)+(1 ? ?)A(G) of a graph G, where D(G) is the degree diagonal matrix and A(G) is the adjacency matrix of G. The ?Spectral Radius of G is the largest eigenvalue of A?(G). For a graph with two pendant paths at a vertex or at two adjacent vertices, we prove results concerning the behavior of the ?Spectral Radius under relocation of a pendant edge in a pendant path. We give upper bounds for the ?Spectral Radius for unicyclic graphs G with maximum degree ? ? 2, connected irregular graphs with given maximum degree and some other graph parameters, and graphs with given domination number, respectively. We determine the unique tree with the second largest ?Spectral Radius among trees, and the unique tree with the largest ?Spectral Radius among trees with given diameter. We also determine the unique graphs so that the difference between the maximum degree and the ?Spectral Radius is maximum among trees, unicyclic graphs and nonbipartite graphs, respectively.

On the distance $\alpha$Spectral Radius of a connected graph
arXiv: Combinatorics, 2019CoAuthors: H.y. Guo, Bo ZhouAbstract:For a connected graph $G$ and $\alpha\in [0,1)$, the distance $\alpha$Spectral Radius of $G$ is the Spectral Radius of the matrix $D_{\alpha}(G)$ defined as $D_{\alpha}(G)=\alpha T(G)+(1\alpha)D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. We give bounds for the distance $\alpha$Spectral Radius, especially for graphs that are not transmission regular, propose some graft transformations that decrease or increase the distance $\alpha$Spectral Radius, and determine the unique graphs with minimum and maximum distance $\alpha$Spectral Radius among some classes of graphs.
Lihua You  One of the best experts on this subject based on the ideXlab platform.

A sharp upper bound for the Spectral Radius of a nonnegative matrix and applications
Czechoslovak Mathematical Journal, 2016CoAuthors: Lihua You, Yujie Shu, Xiaodong ZhangAbstract:We obtain a sharp upper bound for the Spectral Radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency Spectral Radius, the Laplacian Spectral Radius, the signless Laplacian Spectral Radius, the distance Spectral Radius, the distance Laplacian Spectral Radius, the distance signless Laplacian Spectral Radius of an undirected graph or a digraph. These results are new or generalize some known results.

A Sharp upper bound for the Spectral Radius of a nonnegative matrix and applications
arXiv: Combinatorics, 2016CoAuthors: Lihua You, Yujie Shu, Xiaodong ZhangAbstract:In this paper, we obtain a sharp upper bound for the Spectral Radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency Spectral Radius, the Laplacian Spectral Radius, the signless Laplacian Spectral Radius, the distance Spectral Radius, the distance Laplacian Spectral Radius, the distance signless Laplacian Spectral Radius of a graph or a digraph. These results are new or generalize some known results.

Spectral Radius and signless Laplacian Spectral Radius of strongly connected digraphs
arXiv: Combinatorics, 2014CoAuthors: Wenxi Hong, Lihua YouAbstract:Let D be a strongly connected digraph and A(D) be the adjacency matrix of D. Let diag(D) be the diagonal matrix with outdegrees of the vertices of D and Q(D) = diag(D) + A(D) be the signless Laplacian matrix of D. The Spectral Radius of Q(D) is called the signless Laplacian Spectral Radius of D, denoted by q(D). In this paper, we give sharp bound on q(D) with outdegree sequence and compare the bound with some known bounds, establish some sharp upper or lower bound on q(D) with some given parameter such as clique number, girth or vertex connectivity, and characterize the corresponding extremal digraph or proposed open problem. In addition, we also determine the unique digraph which achieves the minimum (or maximum), the second minimum (or maximum), the third minimum, the fourth minimum Spectral Radius and signless Laplacian Spectral Radius among all strongly connected digraphs, and answer the open problem proposed by LinShu [H.Q. Lin, J.L. Shu, A note on the Spectral characterization of strongly connected bicyclic digraphs, Linear Algebra Appl. 436 (2012) 2524{2530].

Spectral Radius and signless Laplacian Spectral Radius of strongly connected digraphs
Linear Algebra and its Applications, 2014CoAuthors: Wenxi Hong, Lihua YouAbstract:Abstract Let D be a strongly connected digraph and A ( D ) be the adjacency matrix of D. Let diag ( D ) be the diagonal matrix with outdegrees of the vertices of D and Q ( D ) = diag ( D ) + A ( D ) be the signless Laplacian matrix of D. The Spectral Radius of Q ( D ) is called the signless Laplacian Spectral Radius of D, denoted by q ( D ) . In this paper, we give a sharp bound on q ( D ) where D has a given outdegree sequence and compare the bound with known bounds. We establish some sharp upper or lower bound on q ( D ) with some given parameter such as clique number, girth or vertex connectivity, and characterize the extremal graph. In addition, we also determine the unique digraph which achieves the minimum (or maximum), the second minimum (or maximum), the third minimum, the fourth minimum Spectral Radius and signless Laplacian Spectral Radius among all strongly connected digraphs, and answer the open problem proposed by Lin and Shu [14] .
Xiaodong Zhang  One of the best experts on this subject based on the ideXlab platform.

A sharp upper bound for the Spectral Radius of a nonnegative matrix and applications
Czechoslovak Mathematical Journal, 2016CoAuthors: Lihua You, Yujie Shu, Xiaodong ZhangAbstract:We obtain a sharp upper bound for the Spectral Radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency Spectral Radius, the Laplacian Spectral Radius, the signless Laplacian Spectral Radius, the distance Spectral Radius, the distance Laplacian Spectral Radius, the distance signless Laplacian Spectral Radius of an undirected graph or a digraph. These results are new or generalize some known results.

A Sharp upper bound for the Spectral Radius of a nonnegative matrix and applications
arXiv: Combinatorics, 2016CoAuthors: Lihua You, Yujie Shu, Xiaodong ZhangAbstract:In this paper, we obtain a sharp upper bound for the Spectral Radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency Spectral Radius, the Laplacian Spectral Radius, the signless Laplacian Spectral Radius, the distance Spectral Radius, the distance Laplacian Spectral Radius, the distance signless Laplacian Spectral Radius of a graph or a digraph. These results are new or generalize some known results.

Spectral Radius of Nonnegative Matrices and Digraphs
Acta Mathematica Sinica English Series, 2002CoAuthors: Xiaodong ZhangAbstract:We present an upper and a lower bound for the Spectral Radius of nonnegative matrices. Then we give the bounds for the Spectral Radius of digraphs.

On the Spectral Radius of Graphs with Cut Vertices
Journal of Combinatorial Theory Series B, 2001CoAuthors: Abraham Berman, Xiaodong ZhangAbstract:We study the Spectral Radius of graphs with n vertices and k cut vertices and describe the graph that has the maximal Spectral Radius in this class. We also discuss the limit point of the maximal Spectral Radius.
Hongying Lin  One of the best experts on this subject based on the ideXlab platform.

The αSpectral Radius of general hypergraphs
Applied Mathematics and Computation, 2020CoAuthors: Hongying Lin, Bo ZhouAbstract:Abstract Given a hypergraph H of order n with rank k ≥ 2, denote by D ( H ) and A ( H ) the degree diagonal tensor and the adjacency tensor of H, respectively, of order k and dimension n. For real number α with 0 ≤ α α D ( H ) + ( 1 − α ) A ( H ) . First, we establish a upper bound on the αSpectral Radius of connected irregular hypergraphs. Then we propose three local transformations of hypergraphs that increase the αSpectral Radius. We also identify the unique hypertree with the largest αSpectral Radius and the unique hypergraph with the largest αSpectral Radius among hypergraphs of given number of pendent edges, and discuss the unique hypertrees with the next largest αSpectral Radius and the unicyclic hypergraphs with the largest αSpectral Radius.

The distance Laplacian Spectral Radius of unicyclic graphs
arXiv: Combinatorics, 2017CoAuthors: Hongying Lin, Bo ZhouAbstract:For a connected graph $G$, the distance Laplacian Spectral Radius of $G$ is the Spectral Radius of its distance Laplacian matrix $\mathcal{L}(G)$ defined as $\mathcal{L}(G)=Tr(G)D(G)$, where $Tr(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. In this paper, we determine the unique graphs with maximum distance Laplacian Spectral Radius among unicyclic graphs.

On distance Spectral Radius of uniform hypergraphs
Linear and Multilinear Algebra, 2017CoAuthors: Hongying Lin, Bo ZhouAbstract:The distance Spectral Radius of a connected hypergraph is the largest eigenvalue of its distance matrix. We determine the unique connected kuniform hypergraphs with minimum distance Spectral Radius when the number of pendant edges is given, the unique kuniform nonhyperstarlike hypertrees (nonhypercaterpillars, respectively) with minimum distance Spectral Radius, and the unique kuniform nonhypercaterpillars with maximum distance Spectral Radius for .

Spectral Radius of uniform hypergraphs
Linear Algebra and its Applications, 2017CoAuthors: Hongying Lin, Bo ZhouAbstract:Abstract We prove a result concerning the behavior of the Spectral Radius of a hypergraph under relocations of edges. We determine the unique hypergraphs with maximum Spectral Radius among connected k uniform hypergraphs with fixed number of pendant edges, the unique k uniform hypertrees with respectively maximum, second maximum and third maximum Spectral Radius, the unique k uniform unicyclic hypergraphs ( k uniform linear unicyclic hypergraphs, respectively) with respectively maximum and second maximum Spectral Radius. We also determine the unique hypergraphs with maximum Spectral Radius among k uniform unicyclic hypergraphs with given girth.

Distance Spectral Radius of uniform hypergraphs
arXiv: Combinatorics, 2016CoAuthors: Hongying Lin, Bo ZhouAbstract:We study the effect of three types of graft transformations to increase or decrease the distance Spectral Radius of uniform hypergraphs, and we determined the unique $k$uniform hypertrees with maximum, second maximum, minimum and second minimum distance Spectral Radius, respectively.
Jinlong Shu  One of the best experts on this subject based on the ideXlab platform.

On the AαSpectral Radius of a graph
Linear Algebra and its Applications, 2018CoAuthors: Jie Xue, Huiqiu Lin, Shuting Liu, Jinlong ShuAbstract:Abstract Let G be a graph with adjacency matrix A ( G ) and let D ( G ) be the diagonal matrix of the degrees of G. For any real α ∈ [ 0 , 1 ] , Nikiforov [3] defined the matrix A α ( G ) as A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) . The largest eigenvalue of A α ( G ) is called the A α Spectral Radius of G. In this paper, we give three edge graft transformations on A α Spectral Radius. As applications, we determine the unique graph with maximum A α Spectral Radius among all connected graphs with diameter d, and determine the unique graph with minimum A α Spectral Radius among all connected graphs with given clique number. In addition, some bounds on the A α Spectral Radius are obtained.

The distance Spectral Radius of digraphs
Discrete Applied Mathematics, 2013CoAuthors: Huiqiu Lin, Jinlong ShuAbstract:Let D([email protected]?) denote the distance matrix of a strongly connected digraph [email protected]?. The eigenvalue of D([email protected]?) with the largest modulus is called the distance Spectral Radius of a digraph [email protected]?, denoted by @r([email protected]?). In this paper, we first give sharp upper and lower bounds for the distance Spectral Radius for strongly connected digraphs; we then characterize the digraphs having the maximal and minimal distance Spectral radii among all strongly connected digraphs; we also determine the extremal digraph with the minimal distance Spectral Radius with given arc connectivity and the extremal digraph with the minimal distance Spectral Radius with given dichromatic number.

Distance Spectral Radius of digraphs with given connectivity
Discrete Mathematics, 2012CoAuthors: Huiqiu Lin, Weihua Yang, Hailiang Zhang, Jinlong ShuAbstract:Let D([email protected]?) denote the distance matrix of a strongly connected digraph [email protected]?. The largest eigenvalue of D([email protected]?) is called the distance Spectral Radius of a digraph [email protected]?, denoted by @r([email protected]?). Recently, many studies proposed the use of @r([email protected]?) as a molecular structure description of alkanes. In this paper, we characterize the extremal digraphs with minimum distance Spectral Radius among all digraphs with given vertex connectivity and the extremal graphs with minimum distance Spectral Radius among all graphs with given edge connectivity. Moreover, we give the exact value of the distance Spectral Radius of those extremal digraphs and graphs. We also characterize the graphs with the maximum distance Spectral Radius among all graphs of fixed order with given vertex connectivity 1 and 2.

On the Spectral Radius of bipartite graphs with given diameter
Linear Algebra and its Applications, 2009CoAuthors: Mingqing Zhai, Ruifang Liu, Jinlong ShuAbstract:Let GB(n,d) be the set of bipartite graphs with order n and diameter d. This paper characterizes the extremal graph with the maximal Spectral Radius in GB(n,d). Furthermore, the maximal Spectral Radius is a decreasing function on d. At last, bipartite graphs with the second largest Spectral Radius are determined.