Bicyclic graphs with the first three smallest and largest values of the first general Zagreb index

Shenggui Zhang, Wei Wang, Edwin Tai Chiu Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

27 Citations (Scopus)

Abstract

Let G be a simple connected graph with vertex set V(G) and α a real number other than 0 and 1. The first general Zagreb index of G is defined as M1α(G) = ΣνεV(G) d(v) α, where d(v) is the degree of v. If G has n vertices and n + 1 edges, then it is called a bicyclic graph. In this paper, for arbitrary n ≥ 5, we characterize all bicyclic graphs on n vertices with the first three smallest and largest values of the first general Zagreb index when α > 1, with the largest and the first three smallest values of the first general Zagreb index when α < 0, and with the smallest and the first three largest values of the first general Zagreb index when 0 < α < 1; for every sufficiently large n, we characterize all bicyclic graphs on n vertices with the second and third smallest values of the first general Zagreb index when 0 < α < 1, and with the second and third largest values of the first general Zagreb index when α < 0.
Original languageEnglish
Pages (from-to)579-592
Number of pages14
JournalMatch
Volume56
Issue number3
Publication statusPublished - 1 Dec 2006

ASJC Scopus subject areas

  • Chemistry(all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this