The irregularity strength and cost of the union of cliques

Stanislav Jendroľ, Michal Tkáč, Z. Tuza

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Assign positive integer weights to the edges of a simple graph with no component isomorphic to Ki or K2, in such a way that the graph becomes irregular, i.e., the weight sums at the vertices become pairwise distinct. The minimum of the largest weights assigned over all such irregular assignments on the vertex-disjoint union of complete graphs is determined. The method of proof also yields the smallest possible total increase in the sum of edge weights in irregular asignments, called irregularity cost.

Original languageEnglish
Pages (from-to)179-186
Number of pages8
JournalDiscrete Mathematics
Volume150
Issue number1-3
Publication statusPublished - Apr 6 1996

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Irregularity Strength
Clique
Union
Irregular
Costs
Irregularity
Simple Graph
Complete Graph
Assign
Pairwise
Disjoint
Assignment
Isomorphic
Distinct
Integer
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

The irregularity strength and cost of the union of cliques. / Jendroľ, Stanislav; Tkáč, Michal; Tuza, Z.

In: Discrete Mathematics, Vol. 150, No. 1-3, 06.04.1996, p. 179-186.

Research output: Contribution to journalArticle

Jendroľ, S, Tkáč, M & Tuza, Z 1996, 'The irregularity strength and cost of the union of cliques', Discrete Mathematics, vol. 150, no. 1-3, pp. 179-186.
Jendroľ, Stanislav ; Tkáč, Michal ; Tuza, Z. / The irregularity strength and cost of the union of cliques. In: Discrete Mathematics. 1996 ; Vol. 150, No. 1-3. pp. 179-186.
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