Authors: Belardo, Francesco
Simić, Slobodan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the Laplacian coefficients of signed graphs
Journal: Linear Algebra and Its Applications
Volume: 475
First page: 94
Last page: 113
Issue Date: 15-Jun-2015
Rank: M21
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.02.007
Abstract: 
Let Γ=(G,σ) be a signed graph, where G is its underlying graph and σ its sign function (defined on edges of G). A signed graphΓ′, the subgraph of Γ, is its signed TU-subgraph if the signed graph induced by the vertices ofΓ′consists of trees and/or unbalanced unicyclic signed graphs. Let L(Γ)=D(G)-A(Γ) be the Laplacian of Γ. In this paper we express the coefficient of the Laplacian characteristic polynomial of Γ based on the signed TU-subgraphs of Γ, and establish the relation between the Laplacian characteristic polynomial of a signed graph with adjacency characteristic polynomials of its signed line graph and signed subdivision graph. As an application, we identify the signed unicyclic graphs having extremal coefficients of the Laplacian characteristic polynomial.
Keywords: Laplacian coefficients | Line graph | Signed graph | Subdivision graph
Publisher: Elsevier
Project: University of Primorska OP RCV_VS-13-25 the operation no. 3330-14-500033
Graph theory and mathematical programming with applications in chemistry and computer science 
PRIN 2012 “Strutture Geometriche, Combinatoria e loro Applicazioni”

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