On the Strong Monophonic Number of a Graph
D. Antony Xavier1, Elizabeth Thomas2, Deepa Mathew3, Santiagu Theresal4
1D.AntonyXaveir, Department of Mathematics, Loyola College, Chennai.. Affiliated to University of Madras, India.
2Elizabeth Thomas, Department of Mathematics, Loyola College, Chennai.. Affiliated to University of Madras, India.
3Deepa Mathew, Department of Mathematics, Loyola College, Chennai Affiliated to University of Madras, India.
4Santiagu Theresal, Department of Mathematics, Loyola College, Chennai.. Affiliated to University of Madras, India.
Manuscript received on September 22, 2019. | Revised Manuscript received on October 20, 2019. | Manuscript published on October 30, 2019. | PP: 1421-1425 | Volume-9 Issue-1, October 2019 | Retrieval Number: A1231109119/2019©BEIESP | DOI: 10.35940/ijeat.A1231.109119
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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: For a connected graph of order at least two, the strong monophonic problem is to determine a smallest set of vertices of such that, by fixing one monophonic path between each pair of the vertices of all vertices of are covered. In this paper, certain general properties satisfied by the strong monophonic sets are studied. Also, the strong monophonic number of a several families of graphs and computational complexity are determined. AMS Subject Classification: 05C12, 05C82
Keywords: Monophonic set, monophonic number, strong monophonic set, strong monophonic number, monophonic distance.