### Abstract

Assign positive integer weights to the edges of a simple graph with no component isomorphic to K_{i} or K_{2}, 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 language | English |
---|---|

Pages (from-to) | 179-186 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 150 |

Issue number | 1-3 |

Publication status | Published - Apr 6 1996 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*150*(1-3), 179-186.

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

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 150, no. 1-3, pp. 179-186.

}

TY - JOUR

T1 - The irregularity strength and cost of the union of cliques

AU - Jendroľ, Stanislav

AU - Tkáč, Michal

AU - Tuza, Z.

PY - 1996/4/6

Y1 - 1996/4/6

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0042632389&partnerID=8YFLogxK

M3 - Article

VL - 150

SP - 179

EP - 186

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -