Balanced group-labeled graphs
β Scribed by Manas Joglekar; Nisarg Shah; Ajit A. Diwan
- Book ID
- 113567456
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 221 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
## 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
We propose a generalization of signed graphs, called group graphs. These are graphs regarded as symmetric digraphs with a group element s(u, u ) called the signing associated with each arc (u, u ) such that s(u, u)s(u, u) = 1. A group graph is ba2anced if the product s(ul, u2)s(u2, ug) -.s(u,, ul) =
Pretzel, 0. and D. Youngs, Balanced graphs and noncovering graphs, Discrete Mathematics, 88 (1991) 279-287. Probabilistic arguments show that triangle-free noncovering graphs are very common. Nevertheless, few specific examples are known. In this paper we describe a simple method of constructing a l