On the signless Laplacian coefficients of unicyclic graphs

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Title:	On the signless Laplacian coefficients of unicyclic graphs
Authors:	Li, Hong-Hai;Tam, Bit-Shun;Li Su
Contributors:	淡江大學數學學系
Keywords:	Signless Laplacian coefficients;Unicyclic graphs;Line graph;Subdivision graph;Matching polynomial;Generalized π-transform;Double τ-transform
Date:	2013-10-01
Issue Date:	2013-09-02 10:53:37 (UTC+8)
Publisher:	Philadelphia: Elsevier Inc.
Abstract:	Let G be a graph of order n and let View the MathML source be the characteristic polynomial of the signless Laplacian of G. Let Eg,n (respectively, Cg(Sn−g+1)) denote the unicyclic graph of order n obtained by a coalescence of a vertex in the cycle Cg with an end vertex (respectively, the center) of the path Pn−g+1 (respectively, the star Sn−g+1). It is proved that for k=2,…,n−1, as G varies over all unicyclic graphs of order n, depending on k and n, the maximum value of pk(G) is attained at G=Cn or E3,n, and the minimum value is attained uniquely at G=C4(Sn−3) or C3(Sn−2). Except for the resolution of a conjecture on cubic polynomials, the uniqueness issue for the maximization problem is also settled.
Relation:	Linear Algebra and its Applications 439(7), pp.2008-2028
DOI:	10.1016/j.laa.2013.05.030
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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