Relatively prime inverse domination of a graph

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DOI:

https://doi.org/10.26637/MJM0804/0167

Abstract

Let GG be non-trivial graph. A subset DD of the vertex set V(G)V(G) of a graph GG is called a dominating set of GG if every vertex in VV - DD is adjacent to a vertex in DD. The minimum cardinality of a dominating set is called the domination number and is denoted by γ(G)γ(G). If VV - D contains a dominating set SS of GG, then SS is called an inverse dominating set with respect to DD. In an inverse dominating set SS, every pair of vertices uu and vv in SS such that (deg uu, deg vv ) =1, then SS is called relatively prime inverse dominating set. The minimum cardinality of a relatively prime inverse dominating set is called relatively prime inverse dominating number and is denoted by γ1rp(G)γ1rp(G). In this paper we find relatively prime inverse dominating number of some graphs.

Keywords:

Domination, Inverse domination, Relatively prime domination

Mathematics Subject Classification:

Mathematics
  • C. Jayasekaran Department of Mathematics, Pioneer Kumaraswamy College Nagercoil-629003, Kanyakumari District, Tamil Nadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti-Tirunelveli-627012.
  • L. Roshini Department of Mathematics, Pioneer Kumaraswamy College Nagercoil-629003, Kanyakumari District, Tamil Nadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti-Tirunelveli-627012.
  • Pages: 2292-2295
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

G. Chartrand, Lesniak: Graphs and Digraphs, fourth ed.,CRC press, BoCa Raton, 2005.

J. A. Gullian: A dynamic survey of graph labeling, The electronics Journal of Combinatories, 17(2014).

W. Haynes, S. T. Hedetniemi, P. J. Slater: Domination in Graphs, Advanced Topices, Marcel Dekker, New York, 1998. DOI: https://doi.org/10.1002/(SICI)1097-0037(199810)32:3<199::AID-NET4>3.0.CO;2-F

S. T. Hedetniemi, R. Laskar (Eds.): Topics in domination in graphs, Discrete Math. 86(1990). DOI: https://doi.org/10.1016/0012-365X(90)90365-O

C. Jayasekaran and A. Jancyvini: Results on relatively prime dominating sets in graphs, Annals of pure and Applied Mathematics, 14, (3), (2017), 359 - 369. DOI: https://doi.org/10.22457/apam.v14n3a2

V. R. Kulli and S. C. Sigarkant: Inverse domination in graphs, Nat. Acad Sci. Letters, 14, (1991), 473-475.

Weisstein, Eric W: Barbell Graph, from Mathworld.

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Published

01-10-2020

How to Cite

C. Jayasekaran, and L. Roshini. “Relatively Prime Inverse Domination of a Graph”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 2292-5, doi:10.26637/MJM0804/0167.