Relatively Prime Inverse Domination On Line Graph

C. Jayasekaran, Roshini L


Let G be non-trivial graph. A subset D of the vertex set V (G) of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D. The minimum cardinality of a dominating set is called the domination number and is denoted by γ(G). If V −D contains a dominating set S of G, then S is called an inverse dominating set with respect to D. In an inverse dominating set S, every pair of vertices u and v in S such that (degu, degv) = 1, then S 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 γ −1 rp (G). In this paper we find relatively prime inverse dominating number of some line graphs.


Domination, Inverse domination, Relatively prime domination.

Full Text:



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

J. A. Gallian, A dynamic survey of graph labeling, The electronic journal of combinatorics, 2021, DS6.

E. Esakkiammal, B. Deepa, K. Thirusangu, Some Labellings on Square Graph of Comb, International Journal of Mathematics Trends and Technology, Special Issue, 2018, 28-30.

J. T. Gross, and Yellen, J. Graph Theory and its Applications, 2nd ed. Boca Raton, FL: CRC Press, 2006.

C. Jayasekaran and A. Jancy vini, Results on relatively prime dominating sets in graphs, Annals of pure and Applied Mathematics, Vol. 14(3), 2017, 359-369.

C. Jayasekaran and L. Roshini, Relatively prime inverse dominating sets in graphs, Malaya Journal of Mathematik, Vol. 8(4), 2020,2292-2295.

J. Jeba Jesitha, N.K. Vinothini and Shahina Munavar Hussain, Odd graceful Labeling for the graph jewel graph and the extended jewel graph without the prime edge, Bulletin of Pure and Applied Sciences Section-E- Mathematics and Statics, Vol. 39E(2), 2020, 212-217.

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

Selvam Avadayappan, M. Bhuvaeshwari, R. Iswariya, γ- Splitting Graphs, International Journal of Reasearch in Applied Science and Engineering Technology, Vol. 4(3), 2016, 670-680.



  • There are currently no refbacks.

Copyright (c) 2023 C. Jayasekaran, Roshini L

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.