The multiplicative reformulated first Zagreb index of some graph operations

M. Aruvi

doi:10.26637/MJM0803/0079

Abstract

In this paper, the multiplicative reformulated first Zagreb index is presented and the sharp upper bound for the multiplicative reformulated first Zagreb index of various graph operations for example, join, composition, cartesian and corona product of graphs are derived.

Keywords:

Topological indices and graph operations

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

M. Aruvi Department of Mathematics, University College of Engineering-BIT Campus, Anna University, Tiruchirappalli-620024, Tamil Nadu, India. https://orcid.org/0000-0002-3090-134X

Pages: 1189-1195
Date Published: 01-07-2020
Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17(1972), 535-538.

Khalifeh, MH, Azari, HY, Ashrafi, AR: The hyperWiener index of graph operations, Comput. Math. Appl., 56(2008), 1402-1407.

Milicevic.ANikolic.S, Trinajstic.N, On Reformulated Zagreb Indices, Discrete Applied Mathematics, 160(2012), 204-209.

Nilanjan De, SK.MD.Abu Nayeem, and Anita Pal, Reformulated First Zagreb Index of Some Graph Operations, Mathematic, 3(2015), 945-960.

V.Sheeba Agnes, Degree distance and Gutman index of corona product of graphs, Transaction on Combinatorics, $4(3)(2015), 11-23$.

G.H. Shirdel, H. Rezapour and A. M. Sayadi, The HyperZagreb index of graph operations, Iranian Journal of Mathematical Chemistry, 2(2013), 213-220.

Todeschini, R, Ballabio, D, Consonni, V: Novel molecular descriptors based on functions of new vertex degrees. In: Gutman, I, Furtula, B (eds.) Novel Molecular Structure Descriptors - Theory and Applications I, 73-100. Univ. Kragujevac, Kragujevac (2010)

Todeschini, R, Consonni, V: New local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem., 64(2010), 359-372.