1. The Cayley sum graph of ideals of a semigroup.
- Author
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Afkhami, Mojgan, Hassankhani, Mehdi, and Khashyarmanesh, Kazem
- Subjects
- *
CAYLEY graphs , *GRAPH connectivity , *UNDIRECTED graphs , *PLANAR graphs - Abstract
Let S be a regular semigroup, J(S) be the set of ideals of S and M be a subset of J(S). In this paper, we introduce an undirected Cayley graph of S, denoted by ΓS,M, with elements of J(S) as the vertex set, and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of M such that IK = J or JK = I. We study some basic properties of the graph ΓS,M such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of ΓS,M. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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