Restricted Detour Polynomials of Some Graphs
ABSTRACT
The restricted detour distance between two vertices and of a connected graph is the length of a longest path in such that The restricted detour polynomial of a graph ,denoted by and defined as follows
where the summation is taken over all unordered pairs of vertices of . The restricted detour index of a connected graph is the Wiener index with respect to restricted detour distance, that is
where the summation is taken over all unordered pairs of vertices in .
The aim of this thesis is to obtain the restricted detour distance and restricted detour polynomials of some particular graphs, namely different classes of ladder graphs such as , and M?bius Ladder and some thorn-cog special graphs such as thorn-ring, cog cycle, thorn-cog cycle, thorn complete, cog complete ,thorn-cog complete, thorn complete-bipartite, cog complete-bipartite, thorn-cog complete-bipartite, thorn wheel, cog wheel, thorn-cog wheel, thorn star, cog star, thorn-cog star. Moreover, the restricted detour indices of most of the particular graphs considered here are obtained. Also the restricted detour diameters for each graph are determined.
posted: 15/03/2017
