Some results on starlike and sunlike graphs
type: Item
instance of: scholarly article
title: Some results on starlike and sunlike graphs
zbMATH Open document ID: 1018.05067
DOI: 10.1007/BF02935725
author: Mirko Lepović
published in: Journal of Applied Mathematics and Computing
publication date: 2003-09-05T00:00:00Z
review text: If \(G\) is a simple graph on vertices \(1,2,\dots,n\), the sunlike graph \(G(k_1,k_2,\dots,k_n)\) is obtained by identifying an end-vertex of a path \(P_{k_i}\), \(k_i\geq 1\), with vertex \(i\) of \(G\), \(i=1,2,\dots,n\). A formula for the characteristic polynomial of a sunlike graph is given and it is shown that, for \(n\geq 3\), whenever graphs \(K_n(k_1,k_2,\dots,k_n)\) and \(K_n(m_1,m_2,\dots,m_n)\) are cospectral, then they are also isomorphic. As a consequence, it is obtained that no two distinct starlike trees are Laplacian cospectral (a tree is starlike if it has exactly one vertex of degree greater than two).
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1907720
zbMATH Keywords: spectrum of graph
zbMATH Keywords: Laplacian characteristic polynomial
MaRDI profile type: Publication
cites work: Q4327350
cites work: A new graph product and its spectrum
cites work: The Laplacian Spectrum of a Graph
cites work: No starlike trees are cospectral
full work available at URL: https://doi.org/10.1007/bf02935725
OpenAlex ID: W2006951722
description: scientific article; zbMATH DE number 1907720