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Information Journal Paper

Title

Some results on vertex-edge Wiener polynomials and indices of graphs

Author(s)

 AZARI M. | Issue Writer Certificate 

Pages

  149-162

Abstract

 The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second vertex-edge Wiener indices of them with each other. Also, we compute these polynomials and indices for some well-known graphs. Then, we study the relation between the vertex-edge Wiener polynomials of Cartesian product of graphs with the Wiener polynomial and vertex-edge Wiener polynomials of the primary graphs and apply the results to compute the vertex-edge Wiener indices of Cartesian product of graphs. As applications of these results, we present exact formulas for computing the first and second vertex-edge Wiener indices of rectangular grids, C4-Nanotubes, C4-nanotori, Hamming graph, and hypercubes.

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    • Cite

    APA: Copy

    AZARI, M.. (2018). Some results on vertex-edge Wiener polynomials and indices of graphs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 4(15 ), 149-162. SID. https://sid.ir/paper/257294/en

    Vancouver: Copy

    AZARI M.. Some results on vertex-edge Wiener polynomials and indices of graphs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;4(15 ):149-162. Available from: https://sid.ir/paper/257294/en

    IEEE: Copy

    M. AZARI, “Some results on vertex-edge Wiener polynomials and indices of graphs,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 4, no. 15 , pp. 149–162, 2018, [Online]. Available: https://sid.ir/paper/257294/en

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