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

Authors

  • N. Dehgardi Department of Mathematics and Computer Science, Sirjan University of Technology, 7813733385, Sirjan, I.R. Iran https://orcid.org/0000-0001-8214-6000
  • S.M. Sheikholeslami Department of Mathematics, Azarbaijan Shahid Madani University, 5375171379, Tabriz, I.R. Iran
  • M. Soroudi Department of Mathematics, Azarbaijan Shahid Madani University, 5375171379, Tabriz, I.R. Iran
https://doi.org/10.15330/cmp.11.2.258-267

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.

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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.