Relatively Prime Detour Domination Number of Some Switching Graphs

Authors

  • C Jayasekaran Associate Professor, Department of Mathematics, Pioneer Kumaraswamy College, Nagercoil - 629003, Tamil Nadu, India
  • L. G. Binoja Department of Mathematics, Pioneer Kumaraswamy College, Nagercoil - 629003, Tamil Nadu, India. Affliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627012, Tamil Nadu, India

DOI:

https://doi.org/10.23755/rm.v48i0.1289

Keywords:

Domination, Detour domination, Relatively prime domination, Relatively prime detour domination, Switching graphs.

Abstract

In this paper, we introduce the concept of relatively prime detour domination number for switching graph. If a set S ⊆ V is a detour set, a dominating set with at least two elements, and has (deg(u), deg(v)) = 1 for each pair of vertices u and v, then it is said to be a relatively prime detour dominating set of a graph G. The relatively prime detour domination number of a graph G is known as γrpdn(G) and represents the lowest cardinality of a relatively prime detour dominating set. First, we explain the concept of a switching graph before producing some conclusions based on the switching graphs of helm, fan, complete, spider, and sunlet graphs that have relatively prime detour domination numbers.

References

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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