On the reduced signless Laplacian spectrum of a degree maximal graph

doi:10.1016/j.laa.2009.11.031

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Title:	On the reduced signless Laplacian spectrum of a degree maximal graph
Authors:	Tam, Bit-Shun;Wu, Shu-Hui
Contributors:	淡江大學數學學系
Keywords:	Degree maximal graph;Reduced signless Laplacian;Signless Laplacian spectrum;Characteristic polynomial;Neighborhood equivalence class
Date:	2010-03-15
Issue Date:	2011-10-01 21:09:37 (UTC+8)
Publisher:	Philadelphia: Elsevier Inc.
Abstract:	For a (simple) graph G, the signless Laplacian of G is the matrix A(G)+D(G), where A(G) is the adjacency matrix and D(G) is the diagonal matrix of vertex degrees of G; the reduced signless Laplacian of G is the matrix Δ(G)+B(G), where B(G) is the reduced adjacency matrix of G and Δ(G) is the diagonal matrix whose diagonal entries are the common degrees for vertices belonging to the same neighborhood equivalence class of G. A graph is said to be (degree) maximal if it is connected and its degree sequence is not majorized by the degree sequence of any other connected graph. For a maximal graph, we obtain a formula for the characteristic polynomial of its reduced signless Laplacian and use the formula to derive a localization result for its reduced signless Laplacian eigenvalues, and to compare the signless Laplacian spectral radii of two well-known maximal graphs. We also obtain a necessary condition for a maximal graph to have maximal signless Laplacian spectral radius among all connected graphs with given numbers of vertices and edges.
Relation:	Linear Algebra and its Applications 432(7), pp.1734-1756
DOI:	10.1016/j.laa.2009.11.031
Appears in Collections:	[Department of Applied Mathematics and Data Science] Journal Article

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