Wiener Index of Total Graph of Some Graphs - Pravin Garg; Shanu Goyal (International Journal of Mathematics And its Applications, 2017)
Let G = (V, E) be a graph. The total graph T(G) of G is that graph whose vertex set is V E, and two vertices are adjacent if and only if they are adjacent or incident in G. For a graph G=(V, E), the graph G.S_m is obtained by identifying each vertex of G by a root vertex of S_m and the graph S_m.G is obtained by identifying each vertex of S_m except root vertex by any vertex of G, where S_m is a star graph with m vertices. In this paper, we consider G as the cycle graph C_n with n vertices and investigate the Wiener index of the total graphs of C_n.S_m and S_n.C_m.