A sharp upper bound on algebraic connectivity using domination number

M. Aouchiche, P. Hansen, D. Stevanović

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let G be a connected graph of order n. The algebraic connectivity of G is the second smallest eigenvalue of the Laplacian matrix of G. A dominating set in G is a vertex subset S such that each vertex of G that is not in S is adjacent to a vertex in S. The least cardinality of a dominating set is the domination number. In this paper, we prove a sharp upper bound on the algebraic connectivity of a connected graph in terms of the domination number and characterize the associated extremal graphs.

Original languageEnglish
Pages (from-to)2879-2893
Number of pages15
JournalLinear Algebra and Its Applications
Volume432
Issue number11
DOIs
Publication statusPublished - Jun 1 2010
Externally publishedYes

Keywords

  • Algebraic connectivity
  • Domination number
  • Extremal graph
  • Laplacian

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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