The determinant of a unicyclic graph's neighborhood matrix
type: Item
instance of: scholarly article
title: The determinant of a unicyclic graph's neighborhood matrix
zbMATH Open document ID: 1075.65065
author: Jianxiang Li
published in: Linear Algebra and its Applications
publication date: 2005-02-23T00:00:00Z
review text: Let \(G\) be a unicyclic graph with \(n\) vertices and a unique cycle, \(A(G)\) denotes the adjacency matrix of the graph \(G\). The algorithm for computing the determinant function of the matrix \(\alpha I_n+A(G)\) which uses \(O(n)\) arithmetic operations under some restrictions on the degrees of the vertices of the graph \(G\) is obtained. Among the corollaries from the above results the author points out the algorithms to compute the determinants of adjacency and neigborhood matrices and the characteristic polynomial for adjacency matrices.
Mathematics Subject Classification ID: 65F40
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 2137779
zbMATH Keywords: adjacency matrix
zbMATH Keywords: neighborhood matrix
zbMATH Keywords: unicyclic graph
zbMATH Keywords: determinant
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: algorithm
reviewed by: Alexander Guterman
MaRDI profile type: Publication
full work available at URL: j.laa.2004.07.012
OpenAlex ID: W2005054814
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DOI: 10.1016/J.LAA.2004.07.012
description: scientific article; zbMATH DE number 2137779