Some bounds on zeroth-order general randic index

Muhammad Kamran Jamil, Ioan Tomescu, Muhammad Imran, Aisha Javed

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

For a graph G without isolated vertices, the inverse degree of a graph G is defined as ID(G) = ∑u2V(G) d(u)-1 where d(u) is the number of vertices adjacent to the vertex u in G. By replacing-1 by any non-zero real number we obtain zeroth-order general Randic index, i.e., 0Rγ(G) = ∑u2V(G) d(u)γ, where γ ∈ R-System. Text. UTF8Encoding. Xu et al. investigated some lower and upper bounds on ID for a connected graph γ in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0. The corresponding extremal graphs have also been identified.

Original languageEnglish
Article number98
JournalMathematics
Volume8
Issue number1
DOIs
Publication statusPublished - Jan 1 2020

Keywords

  • Extremal graphs
  • Graph parameters
  • Inverse degree
  • Zeroth order general Randic index

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Engineering (miscellaneous)
  • General Mathematics

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