A Face Change of Monophonic Dominating Sets by Non-Adjacency in Graphs
A. Sadiquali1, P. Arul Paul Sudhahar2
1A. Sadiquali, Research Scholar, Alagappa University, Karaikudi (Tamil Nadu), India.
2P. Arul Paul Sudhahar, Department of Mathematics, Rani Ann Govt. College (W), Tirunelveli (Tamil Nadu, India.
Manuscript received on 01 May 2019 | Revised Manuscript received on 15 May 2019 | Manuscript published on 30 May 2019 | PP: 1233-1237 | Volume-8 Issue-7, May 2019 | Retrieval Number: G6360058719/19©BEIESP
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Abstract: The concept of an independent domination number (id-number in short) of a graph is related to the movements of a chessboard. In this paper, we extend the notion of id-number into an independent monophonic domination number of graphs (abridged as imd-number) by introducing chordless paths and non-adjacency property among vertices. The imd-number can be used to optimize the number of mutually non-attacking queens in the play of Chessboard. Discussed the face changing process of monophonic dominating sets by non-adjacency property and some of its properties are studied. It is shown that for with and there exists connected graphs such that, monophonic diameter of and imd- number. Also, for with, there exists connected graphs such that and. The imd-number of certain common class of graphs are determined.
Keyword: Monophonic Domination Number, Independence Number, Independent Monophonic Domination Number and Independent Monophonic Dominating sets.
Scope of the Article: Applied Mathematics and Mechanics.