Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3089 2022 2022 University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China Lee Lee Computer Techniques Engineering Department, Al-Mustaqbal University, Babil, Iraq Ahmed Jubbori 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. 2024 2024 25 34 10.54216/GJMSA.0110103 https://www.americaspg.com/articleinfo/33/show/3089