Coefficients of the characteristic polynomial of the (signless, normalized) Laplacian of a graph
type: Item
instance of: scholarly article
title: Coefficients of the characteristic polynomial of the (signless, normalized) Laplacian of a graph
zbMATH Open document ID: 1380.05122
author: Peng Zhang
published in: Graphs and Combinatorics
publication date: 2017-12-12T00:00:00Z
review text: Researchers worldwide were rigorously looking for isomorphism invariants and their endeavor has culminated in the development of algebraic properties of the different matrices of a graph such as adjacency matrix, signless matrix, Laplacian matrix, normalized matrix and so on. Specifically, they studied in deep the coefficients of the characteristic polynomial of these matrices. From their analysis, the authors give the fifth coefficient of the Laplacian characteristic polynomial and of the signless Laplacian characteristic polynomial and the first five coefficients of the normalized Laplacian characteristic polynomial of a graph. The authors draw inspiration from the result of Kelmans that Laplacian coefficients can be expressed in terms of subtree structures of \(G\) (see [\textit{A. K. Kelmans} and \textit{V. M. Chelnokov}, J. Comb. Theory, Ser. B 16, 197--214 (1974; Zbl 0277.05104)]). The results are quite interesting and easily comprehensible.
reviewed by: V. Yegnanarayanan
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C31
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6817808
zbMATH Keywords: signlessmatix
zbMATH Keywords: normalized matrix
zbMATH Keywords: Laplacian matrix
zbMATH Keywords: Laplacian characteristic polynomial
zbMATH Keywords: coefficient
zbMATH Keywords: graph
MaRDI profile type: Publication
full work available at URL: s00373-017-1831-2
OpenAlex ID: W2736620986
cites work: Spektren endlicher Grafen
cites work: Signless Laplacians of finite graphs
cites work: A certain polynomial of a graph and graphs with an extremal number of trees
cites work: No starlike trees are cospectral
cites work: On the signless Laplacian coefficients of unicyclic graphs
cites work: On the Laplacian coefficients of acyclic graphs
cites work: The characteristic polynomial of a graph
cites work: The characteristic polynomial of the Laplacian of graphs in (\(a\), \(b\))-linear classes
cites work: Q4304296
cites work: Some results on the signless Laplacians of graphs
cites work: On the spectral characterizations of \(\infty \)-graphs
cites work: On the spectral characterizations of 3-rose graphs
DOI: 10.1007/S00373-017-1831-2
description: scientific article; zbMATH DE number 6817808