Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 11 , Issue 1 , PP: 25-34, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Lee Xu, Taher 1 * , Ahmed Jubbori 2
Doi: https://doi.org/10.54216/GJMSA.0110103
Let u and v be any two distinct vertices in a connected graph G. A container C(u,v) is a set of internally disjoint u - v paths. The width of C(u,v) is denoted by w or w(C(u,v)), it is equal to , and the length of is the length of the longest u – v path in C(u,v). Then, for a given positive integer w, the width distance between any two distinct vertices u and v in a connected graph G is define by:dw (u,v)=min/(C(u,v)) l(C(u,v)) , where the minimum is taken over all containers C(u, v) of width w.In this paper, we find the Hosoya polynomials and Wiener indices of the join of two special graphs such as bipartite complete graphs, paths, cycles, star graphs and wheel graphs with respect to the width distance.
Connected graph , Path, Width , Hosoya polynomial
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