## Abstract Given a graph Ξ an abelian group __G__, and a labeling of the vertices of Ξ with elements of __G__, necessary and sufficient conditions are stated for the existence of a labeling of the edges in which the label of each vertex equals the product of the labels of its incident edges. Such
Pair Labelings of Graphs
β Scribed by Guichard, David R.; Krussel, John W.
- Book ID
- 118199384
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1992
- Tongue
- English
- Weight
- 783 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0895-4801
- DOI
- 10.1137/0405012
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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 intro
## Abstract A strongly harmonious labeling is the nonmodular version of a harmonious labeling. The windmill graph __K__^(__t__^)~__n__~ is the graph consisting of __t__ copies of the complete graph __K~n~__ with a vertex in common. It is shown that, for __t__ β₯ 1, __K__^(__t__^)~__n__~ is strongly