A Sharp Upper Bound on Algebraic Connectivity Using Domination Number
نویسندگان
چکیده
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.
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Article history: Received 8 July 2009 Accepted 4 September 2009 Available online 7 October 2009 Submitted by R.A. Brualdi AMS classification: 5C50 15A48 05C05
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