Domination of Cayley Digraph and its Complement
R. Rajeswari1, R. Udhaya Shree2, M. Nirmala3
1R. Rajeswari, Sathyabama Institute of Science and Technology, Chennai (Tamil Nadu), India.
2R. Udhaya Shree, Sathyabama Institute of Science and Technology, Chennai (Tamil Nadu), India.
3M. Nirmala, Sathyabama Institute of Science and Technology, Chennai (Tamil Nadu), India.
Manuscript received on 21 October 2019 | Revised Manuscript received on 25 October 2019 | Manuscript Published on 02 November 2019 | PP: 4005-4008 | Volume-8 Issue-2S11 September 2019 | Retrieval Number: B15450982S1119/2019©BEIESP | DOI: 10.35940/ijrte.B1545.0982S1119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: A Cayley graph constructed out of a group Γ and its generating set A is denoted by Cay (Γ, A). The digraph with the same node set as the original digraph is said to be a complement digraph if it has an edge from x to y exactly when the original digraph does not have an edge from x to y. A subset Ɖ of V is called a dominating set if each vertex in V- Ɖ is adjacent to at least one vertex in Ɖ. The minimum cardinality of a dominating set is called Domination number which is denoted by γ. The domination number of Cayley digraphs and Complement of Cayley digraphs of groups are investigated in this paper. Also, the graph relationship involving domination parameters in a graph and its complement are studied.
Keywords: Cayley Digraph; Complement of a Graph; Domination Number; Alternating Group.
Scope of the Article: Graph Algorithms and Graph Drawing