✦ LIBER ✦

The irregularity strength of tKp

✍ Scribed by Stanislav Jendroľ; Michal Tkáč

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 211 KB
Volume: 145
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)e0043-h

No coin nor oath required. For personal study only.

✦ Synopsis

Assign positive integer weights to the edges of a simple graph G (with no isolated edges and vertices) of order at least 3 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 union of t copies of the complete graph with p vertices, p >~ 3, is determined. A recent conjecture of Faudree et al. is disproved.

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