Characteristic polynomials of some graph coverings
type: Item
instance of: scholarly article
title: Characteristic polynomials of some graph coverings
zbMATH Open document ID: 0835.05044
DOI: 10.1016/0012-365X(94)00024-D
author: Hirobumi Mizuno
author: Iwao Sato
published in: Discrete Mathematics
publication date: 1995-08-27T00:00:00Z
review text: Finite simple undirected graphs \(G = G(V,E)\) and their adjacency matrices \(A(G)\) are considered. By the characteristic polynomial \(\Phi (G; \lambda)\) of \(G\) we understand the determinant of \(\lambda I - A(G)\). Let \(D(G)\) be the set of the \(2 |E |\) directed edges (between elements of \(V)\) such that we take \((u,v)\) and \((v,u)\) for any element \([u,v]\) of \(E\). The authors introduce a graph \(G^\alpha\), called the derived graph of \((G, \alpha)\) [or a derived graph covering of \(G\) with voltages in \(\Gamma]\), where \(\alpha\) is a mapping of \(D(G)\) to a finite group \(\Gamma\) and \(\alpha (v,u) = (\alpha (u,v))^{-1}\) is postulated for any pair of adjacent vertices of \(G\). It is shown that \(\Phi (G^\alpha; \lambda)\) is divisible by \(\Phi (G; \lambda)\), the quotient polynomial is determined in terms of the irreducible representation of \(\Gamma\) and the Kronecker product of matrices.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 790769
zbMATH Keywords: characteristic polynomials
zbMATH Keywords: adjacency matrices
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: derived graph
zbMATH Keywords: graph covering
zbMATH Keywords: quotient polynomial
zbMATH Keywords: irreducible representation
zbMATH Keywords: Kronecker product
reviewed by: A. Ádám
MaRDI profile type: Publication
cites work: Q5586503
cites work: Q4712950
cites work: Caracteristics polynomials of some grap bundlesII
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cites work: Characteristic polynomials of some weighted graph bundles and its application to links
description: scientific article; zbMATH DE number 790769