Some distance based indices of graphs based on four new operations related to the lexicographic product - Dehgardi, N.; Sheikholeslami, S.M.; Soroudi, M. (Carpathian Mathematical Publications, 2019)
For a (molecular) graph, the Wiener index, hyper-Wiener index and degree distance index are defined as W(G)= _{u,v}V(G)d_G(u,v), WW(G)=W(G)+_{u,v}V(G) d_G(u,v)^2, and DD(G)=_{u,v}V(G)d_G(u, v)(d(u/G)+d(v/G)), respectively, where d(u/G) denotes the degree of a vertex u in G and d_G(u, v) is distance between two vertices u and v of a graph G. In this paper, we study Wiener index, hyper-Wiener index and degree distance index of graphs based on four new operations related to the lexicographic product, subdivision and total graph.