متعددات حدود هوسويا-w لاتصال بعض البيانات الخاصة

Abstract EN

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)) is C(u, v) , and the length of (C(u,v)) 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: ( , ) min ( ( , )) ( , ) d u v C u v w 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.