Authors: | Aouchiche, Mustapha Hansen, Pierre Stevanović, Dragan |
Title: | A sharp upper bound on algebraic connectivity using domination number | Journal: | Linear Algebra and Its Applications | Volume: | 432 | Issue: | 11 | First page: | 2879 | Last page: | 2893 | Issue Date: | 1-Jun-2010 | Rank: | M22 | ISSN: | 0024-3795 | DOI: | 10.1016/j.laa.2009.12.031 | 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. |
Keywords: | Algebraic connectivity | Domination number | Extremal graph | Laplacian | Publisher: | Elsevier |
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