The sharp bounds on general sum-connectivity index of four operations on graphs

Shehnaz Akhter, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)

Abstract

The general sum-connectivity index χα( G) , for a (molecular) graph G, is defined as the sum of the weights (dG(a1)+dG(a2))α of all a1a2∈ E( G) , where dG( a1) (or dG( a2) ) denotes the degree of a vertex a1 (or a2) in the graph G; E( G) denotes the set of edges of G, and α is an arbitrary real number. Eliasi and Taeri (Discrete Appl. Math. 157:794-803, 2009) introduced four new operations based on the graphs S( G) , R( G) , Q( G) , and T( G) , and they also computed the Wiener index of these graph operations in terms of W( F( G) ) and W( H) , where F is one of the symbols S, R, Q, T. The aim of this paper is to obtain sharp bounds on the general sum-connectivity index of the four operations on graphs.

Original languageEnglish
Article number241
JournalJournal of Inequalities and Applications
Volume2016
Issue number1
DOIs
Publication statusPublished - Dec 1 2016

Keywords

  • Cartesian product
  • General sum-connectivity index
  • Operation on graphs
  • Total graph

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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