✦ LIBER ✦

On sequential labelings of graphs

✍ Scribed by Thom Grace

Publisher: John Wiley and Sons
Year: 1983
Tongue: English
Weight: 276 KB
Volume: 7
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190070208

No coin nor oath required. For personal study only.

✦ Synopsis

A valuation on a simple graph G IS an assignment of labels to the vertices of G which induces an assignment of labels to the edges of G. pvaluations, also called graceful labelings, and a-valuations, a subclass of graceful labelings, have an extensive literature; harmonious labelings have been introduced recently by Graham and Sloane. This paper introduces sequential labelings, a subclass of harmonious labelings, and shows that any tree admitting an a-valuation also admits a sequential labeling and hence is harmonious. Constructions are given for new families of graceful and sequential graphs, generalizing some earlier results. Finally, a conjecture of Frucht is shown to be wrong by exhibiting several graceful labelings of wheels in which the center label is larger than previously thought possible.

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