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