The irregularity strength and cost of the union of cliques
type: Item
instance of: scholarly article
title: The irregularity strength and cost of the union of cliques
zbMATH Open document ID: 0852.05054
DOI: 10.1016/0012-365X(95)00186-Z
author: Michal Tkáč
author: Zsolt Tuza
author: Stanislav Jendroľ
published in: Discrete Mathematics
publication date: 1996-07-02T00:00:00Z
review text: A network \(G(w)\) consists of a graph \(G\) together with a mapping \(w\) of its edge set into the set of positive integers; the value \(w(e)\) is called the weight of the edge \(e\). The strength \(s(G(w))\) of the network \(G(w)\) is the maximum of \(w(e)\) over all edges \(e\) of \(G\). The weighted degree of a vertex \(x\) of \(G\) is the sum of weights of edges which are incident to \(x\). If no two vertices have the same weighted degree, the network \(G(w)\) is called irregular. The irregularity strength \(s(G)\) of \(G\) is the minimum of \(s(G(w))\) over all irregular networks \(G(w)\) with the underlying graph \(G\). A similar concept is the irregularity cost. The main result of the paper is the theorem determining the irregularity strength of the disjoint union \(\bigcup^n_{i= 1} t_i K_{p_i}\) of cliques. Some results concerning the irregularity cost are added.
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 895998
zbMATH Keywords: network
zbMATH Keywords: irregularity strength
zbMATH Keywords: irregularity cost
MaRDI profile type: Publication
cites work: Q3824455
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description: scientific article; zbMATH DE number 895998