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Adjacent Vertex

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Zhang Zhong-fu – One of the best experts on this subject based on the ideXlab platform.

  • The Adjacent Vertex Distinguishing Vertex-Edge Total Coloring of Some Join Graphs
    Mathematics in Practice and Theory, 2011
    Co-Authors: Zhang Zhong-fu
    Abstract:

    Let G(V,E) is a simple graph,k is a positive integer.A mapping f from V(G)∪E(G) to {1,2,…,k} is called the Adjacent Vertex distinguishing Vertex-edge total coloring of G iff■uv∈E(G),f(u)≠f(uv),f(v)≠f(uv),■uv∈E(G),C(u)≠C(v) and the minimum number of k is called the Adjacent Vertex distinguishing Vertex-edge total chromatic number of G,where C(u) = {f(u)}∪{f(uv)|uv G E(G)}.In this paper,the Adjacent Vertex distinguishing Vertex-edge total coloring is studied,the Adjacent Vertex distinguishing Vertexedge total chromatic number of the join graph of some spatial graphs is obtained.

  • Smarandachely Adjacent Vertex Edge of Graph P_m+P_n
    Journal of Luoyang Institute of Science and Technology, 2010
    Co-Authors: Zhang Zhong-fu
    Abstract:

    Let G be a simple graph,k is a positive integer.f is a mapping from V(G)∪E(G) to {1,2,…,k} and if f follows the following formulas:(1)u v,uw∈E(G),v≠w,f(uv)≠f(u w);(2)uv ∈E(G),|C(u)\C(v)|≥1 and|C(v)\C(u)|≥ 1,we say that Pm + Pn is called the smarandachely Adjacent Vertex edge of graph χs’a(G)=n+2.The minimal number of χs’a(G)=n+2 is called the smarandachely Adjacent Vertex edge chromatic number of χs’a(G)=n+2,The smarandachely Adjacent Vertex edge number on the join-graph of m-order path(m=2,3,4) and n-order path has been given.Among which we can see that C(u)={f(uv)|uv∈E(G)且u≠v}.

  • On Adjacent Vertex-distinguishing-equitable Total Coloring of Double Graphs
    , 2009
    Co-Authors: Zhang Zhong-fu
    Abstract:

    We studied Adjacent Vertex-distinguishing-equitable total coloring(AVDETC) of some double graphs,and developed the Adjacent Vertex-distinguishing-equitable total chromatic numbers of double graphs of even order complete graph,even order cycle,path,star and wheel using constructive method and matching method,which satisfies the conjecture on AVDETCC.

Zhong-fu Zhang – One of the best experts on this subject based on the ideXlab platform.

  • On the Adjacent Vertex-distinguishing acyclic edge coloring of some graphs
    Applied Mathematics-A Journal of Chinese Universities, 2011
    Co-Authors: Wai Chee Shiu, Wai Hong Chan, Zhong-fu Zhang, Liang Bian
    Abstract:

    A proper edge coloring of a graph G is called Adjacent Vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv ∈ E(G). The Adjacent Vertex distinguishing acyclic edge chromatic number of G, denoted by x′Aa(G), is the minimal number of colors in an Adjacent Vertex distinguishing acyclic edge coloring of G. If a graph G has an Adjacent Vertex distinguishing acyclic edge coloring, then G is called Adjacent Vertex distinguishing acyclic. In this paper, we obtain Adjacent Vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.

  • The Smarandachely Adjacent–Vertex distinguishing total coloring of two kind of 3-regular graphs
    2010 3rd International Conference on Biomedical Engineering and Informatics, 2010
    Co-Authors: Zhiwen Wang, Fei Wen, Zhong-fu Zhang
    Abstract:

    The Smarandachely Adjacent–Vertex distinguishing total coloring of graphs is a proper k-total coloring such that every Adjacent Vertex coloring set not embrace each other, the minimal number k is denoted the Smarandachely Adjacent–Vertex distinguishing total coloring chromatic number of graphs. Where the coloring set include the colors of all edges incident to the Vertex plus the color of it. In this paper, we construct two kind of 3-regular graph R n 3 and S 4n 3, and obtain the Smarandachely Adjacent–Vertex distinguishing total coloring chromatic number of it.

  • Adjacent Vertex reducible edge total coloring of graphs
    BioMedical Engineering and Informatics, 2009
    Co-Authors: Zhong-fu Zhang, Enqiang Zhu, Fei Wen, Ji Zhang
    Abstract:

    Let G(V,E) be a simple graph,k (1 k + 1) is a positive integer. f is a mapping from V (G) [ E(G) to {1,2,…,k} such that 8uv,uw 2 E(G),v 6= w,f(uv) 6= f(uw);8uv 2 E(G) , if d(u) = d(v)then C(u) = C(v);we say that f is the Adjacent Vertex reducible edge-total coloring of G. The maximum number of k is called the Adjacent Vertex reducible edge-total chromatic number of G, simply denoted by avret(G). Where C(u) = {f(u)|u 2 V (G)} [ {f(uv)|uv 2 E(G)}. In this paper,the Adjacent Vertex reducible edge-total chromatic number of some special graphs.

Fei Wen – One of the best experts on this subject based on the ideXlab platform.

  • The algorithm for Adjacent Vertex distinguishing proper edge coloring of graphs
    Discrete Mathematics Algorithms and Applications, 2015
    Co-Authors: Fei Wen
    Abstract:

    An Adjacent Vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of Adjacent vertices meet the same set of colors. The minimum number of colors is called Adjacent Vertex distinguishing proper edge chromatic number of G. In this paper, we present a new heuristic intelligent algorithm to calculate the Adjacent Vertex distinguishing proper edge chromatic number of graphs. To be exact, the algorithm establishes two objective subfunctions and a main objective function to find its optimal solutions by the conditions of Adjacent Vertex distinguishing proper edge coloring. Moreover, we test and analyze its feasibility, and the test results show that this algorithm can rapidly and efficiently calculate the Adjacent Vertex distinguishing proper edge chromatic number of graphs with fixed order, and its time complexity is less than O(n3).

  • The algorithm for Adjacent Vertex distinguishing proper edge coloring of graphs
    Discrete Mathematics Algorithms and Applications, 2015
    Co-Authors: Fei Wen
    Abstract:

    An Adjacent Vertex distinguishing proper edge coloring of a graph [Formula: see text] is a proper edge coloring of [Formula: see text] such that no pair of Adjacent vertices meet the same set of colors. The minimum number of colors is called Adjacent Vertex distinguishing proper edge chromatic number of [Formula: see text]. In this paper, we present a new heuristic intelligent algorithm to calculate the Adjacent Vertex distinguishing proper edge chromatic number of graphs. To be exact, the algorithm establishes two objective subfunctions and a main objective function to find its optimal solutions by the conditions of Adjacent Vertex distinguishing proper edge coloring. Moreover, we test and analyze its feasibility, and the test results show that this algorithm can rapidly and efficiently calculate the Adjacent Vertex distinguishing proper edge chromatic number of graphs with fixed order, and its time complexity is less than [Formula: see text].

  • The Smarandachely Adjacent–Vertex distinguishing total coloring of two kind of 3-regular graphs
    2010 3rd International Conference on Biomedical Engineering and Informatics, 2010
    Co-Authors: Zhiwen Wang, Fei Wen, Zhong-fu Zhang
    Abstract:

    The Smarandachely Adjacent–Vertex distinguishing total coloring of graphs is a proper k-total coloring such that every Adjacent Vertex coloring set not embrace each other, the minimal number k is denoted the Smarandachely Adjacent–Vertex distinguishing total coloring chromatic number of graphs. Where the coloring set include the colors of all edges incident to the Vertex plus the color of it. In this paper, we construct two kind of 3-regular graph R n 3 and S 4n 3, and obtain the Smarandachely Adjacent–Vertex distinguishing total coloring chromatic number of it.

Shunqin Liu – One of the best experts on this subject based on the ideXlab platform.

  • Smarandachely Adjacent Vertex Distinguishing Edge Coloring of Some Graphs
    Journal of Physics: Conference Series, 2019
    Co-Authors: Shunqin Liu
    Abstract:

    A Series of new coloring problems (such as Vertex distinguishing edge coloring, Vertex distinguishing total coloring, Adjacent Vertex distinguishing edge coloring, smarandachely Adjacent Vertex distinguishing edge coloring)arise with the divelopment of computer science and information science. At present, there are relatively few articles on smarandachely Adjacent Vertex distinguishing edge coloring. This paper was to solve the problem of the smarandachely Adjacent Vertex distinguishing edge coloring of graph C 2m ×C n .

  • Smarandachely Adjacent–Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn
    viXra, 2017
    Co-Authors: Shunqin Liu
    Abstract:

    According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, Adjacent–Vertex-distinguishing total chromatic number, Adjacent–Vertex-distinguishing proper edge chromatic number, smarandachely-Adjacent–Vertex-distinguishing proper edge chromatic number, smarandachely-Adjacent–Vertex-distinguishing proper total chromatic number.

  • smarandachely Adjacent Vertex distinguishing proper edge chromatic number of cm kn
    viXra, 2017
    Co-Authors: Shunqin Liu
    Abstract:

    According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, Adjacent–Vertex-distinguishing total chromatic number, Adjacent–Vertex-distinguishing proper edge chromatic number, smarandachely-Adjacent–Vertex-distinguishing proper edge chromatic number, smarandachely-Adjacent–Vertex-distinguishing proper total chromatic number.

Qing Yang – One of the best experts on this subject based on the ideXlab platform.

  • Adjacent Vertex Distinguishing Edge-colorings of the Lexicographic Product of Special Graphs
    DEStech Transactions on Computer Science and Engineering, 2018
    Co-Authors: Langwangqing Suo, Shuang Liang Tian, Qing Yang
    Abstract:

    A class of special graphs n W including wheels, fans and stars is defined. Afterwards, the Adjacent Vertex distinguishing edge-coloring of lexicographic product G[H] of graph class n W and any graph G is studied, and gives an upper bound of the chromatic number of coloring, For special H , the exact value of the Adjacent Vertex distinguishing edge-coloring of G[H] is obtained. In this paper, we prove that the chromatic number of Adjacent Vertex distinguishing edge-coloring of lexicographic product G[H] for any two graphs G and H is equal to the graph class n W .