Some distance based indices of graphs based on four new operations related to the lexicographic product

Keywords:
Wiener index, degree distance index, hyper-Wiener index, lexicographic product, subdivision, total graph
Published online:
2019-12-31
Abstract
For a (molecular) graph, the Wiener index, hyper-Wiener index and degree distance index are defined as W(G)=∑{u,v}⊆V(G)dG(u,v), WW(G)=W(G)+∑{u,v}⊆V(G)dG(u,v)2, and DD(G)=∑{u,v}⊆V(G)dG(u,v)(d(u/G)+d(v/G)), respectively, where d(u/G) denotes the degree of a vertex u in G and dG(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.
How to Cite
(1)
Dehgardi, N.; Sheikholeslami, S.; Soroudi, M. Some Distance Based Indices of Graphs Based on Four New Operations Related to the Lexicographic Product. Carpathian Math. Publ. 2019, 11, 258-267.