Domination in Cayley Digraphs of Right and Left Groups

Authors

  • Nuttawoot Nupo Department of Mathematics, Chiang Mai University, Huay Kaew Road, Chiang Mai, Thailand, 5020
  • Sayan Panma Department of Mathematics, Chiang Mai University, Huay Kaew Road, Chiang Mai, Thailand, 5020

DOI:

https://doi.org/10.26713/cma.v8i3.532

Keywords:

Cayley digraph, Right group, Left group, Domination number, Total domination number

Abstract

Let Cay(S,A) denote a Cayley digraph of a semigroup S with a connection set A. A semigroup S is said to be a right group if it is isomorphic to the direct product of a group and a right zero semigroup and S is called a left group if it is isomorphic to the direct product of a group and a left zero semigroup. In this paper, we attempt to nd the value or bounds for the domination number of Cayley digraphs of right groups and left groups. Some examples which give sharpness of those bounds are also shown. Moreover, we consider the total domination number and give the necessary and sufficient conditions for the existence of total dominating sets in Cayley digraphs of right groups and left groups.

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Published

30-12-2017
CITATION

How to Cite

Nupo, N., & Panma, S. (2017). Domination in Cayley Digraphs of Right and Left Groups. Communications in Mathematics and Applications, 8(3), 271–287. https://doi.org/10.26713/cma.v8i3.532

Issue

Vol. 8 No. 3 (2017)

Section

Research Article

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