Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 423, Issue 1, Pages 53-73Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2006.08.017
Keywords
Laplacian of graph; algebraic connectivity; vertex and edge connectivities; bounds for the algebraic connectivity; fiedler vectors; limit points; extremal graphs; Laplacian integral graphs
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This paper is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best-known as the algebraic connectivity of G, denoted a (G). Emphasis is given on classifications of bounds to algebraic connectivity as a function of other graph invariants, as well as the applications of Fiedler vectors (eigenvectors realated to a(G)) on trees, oil hard problems in graphs and also oil the combinatorial optimization problems. Besides, limit points to a(G) and characterizations of extremal graphs to a(G) are described, especially those for which the algebraic connectivity is equal to the vertex connectivity. (C) 2006 Elsevier Inc. All rights reserved.
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