Results on Relatively Prime Domination Number of Vertex Switching of Some Graphs

A Jancy Vini, C Jayasekaran

Abstract


If a set S ⊆ V has at least two members and every pair of vertices u and v is such that (d(u), d(v)) = 1, then it is said to be a relatively prime dominating set. The relatively prime domination number, represented by γrpd(G), is the lowest cardinality of a relatively prime dominating set. The switching of a finite undirected graph by a subset is defined as the graph Gσ(V, E′), which is obtained from G by removing all edges between σ and its complement V − σ and adding as edges all non-edges between σ and V − σ. In this paper, we com-
pute the relatively prime domination number of vertex switching of cycle type graphs like David Star Graph, Helm Graph, Friendship Graph and Book Graph.


Keywords


Dominating set, Relatively prime dominating set, Relatively prime domination number, Vertex switching

Full Text:

PDF

References


C. Berge. "Theory of Graphs and its Applications." London, 1962.

F. Harary. "Graph Theory." Addison-Wesley, Redwood City, 1972.

P.J. Slater, T.W. Haynes, S.T. Hedetniemi. "Fundamentals of Domination in Graphs." Marcel Dekker, Inc., New York, 1998.

C. Jayasekaran. "Self-vertex switching of disconnected unicyclic graphs." Ars Combinatoria, 129, 2016.

A. Jancy Vini, C. Jayasekaran. "Relatively Prime Dominating Sets in Graphs." Annals of Pure and Applied Mathematics, 14(3), 2017.

A. Jancy Vini, C. Jayasekaran. "Relatively prime dominating polynomial in graphs." Malaya Journal of Matematik, 7(4), 2019.

A. Jancy Vini, C. Jayasekaran. "Results on relatively prime domination polynomial of some graphs." Malaya Journal of Matematik, S(1), 2020.

J. H. Lint and J. J. Seidel. "Equilateral points in elliptic geometry." In Proc. Kon. Nede. Acad. Wetensch., Ser. A, 69, 1966.

O. Ore. "Theory of Graphs." Amer. Math. Soc. Colloq. Publ., 38(Amer. Math. Soc., Providence, RI), 1962.

Wu Baoyindureng Meng Jixiang. "Equilateral points in elliptic geometry. Basic Properties of Total Transformation Graphs, 34(2), 2001.




DOI: http://dx.doi.org/10.23755/rm.v48i0.1211

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 A Jancy Vini, C Jayasekaran

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.