Hoffman-type identities
type: Item
instance of: scholarly article
title: Hoffman-type identities
zbMATH Open document ID: 1041.05048
DOI: 10.1016/S0893-9659(03)80047-2
author: Dragan Stevanović
author: Andreas W. M. Dress
published in: Applied Mathematics Letters
publication date: 2004-06-11T00:00:00Z
review text: Let \(G\) be a simple graph and let \(A\) be the adjacency matrix of \(G\). Hoffman observed that \(G\) is a connected regular graph if and only if there exists a polynomial \(P(x)\) such that \(P(A) = J\), where \(J\) is the \(n\times n\) all-one matrix. In this work the authors generalize the Hoffman identity and derive corresponding identities for the recently introduced classes of harmonic and semiharmonic graphs.
reviewed by: Mirko Lepović
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 2073779
zbMATH Keywords: Hoffman's identity
zbMATH Keywords: regular graphs
zbMATH Keywords: harmonic graphs
zbMATH Keywords: semiharmonic graphs
zbMATH Keywords: adjacency matrix
MaRDI profile type: Publication
cites work: On the Polynomial of a Graph
cites work: Eigenspaces of graphs
cites work: The number of standard and of effective multiple alignments
cites work: Semiharmonic trees and monocyclic graphs
cites work: Asymptotic results regarding the number of walks in a graph
cites work: Harmonic trees
cites work: The Polynomial of a Directed Graph
full work available at URL: s0893-9659(03)80047-2
OpenAlex ID: W2091181333
description: scientific article; zbMATH DE number 2073779