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Some results on vertex-edge Wiener polynomials and indices of graphs | ||
Journal of New Researches in Mathematics | ||
مقاله 13، دوره 4، شماره 15، بهمن 2018، صفحه 149-162 اصل مقاله (12.13 M) | ||
نوع مقاله: research paper | ||
نویسنده | ||
M. azari | ||
Assistant Professor, Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box:73135-168, Kazerun, Iran | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Topological index؛ Cartesian product of graphs؛ Nanotube؛ Nanotorus | ||
مراجع | ||
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