Relatively Prime Detour Domination Number of Some Switching Graphs

C Jayasekaran, L. G. Binoja

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.

Keywords


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

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References


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DOI: http://dx.doi.org/10.23755/rm.v48i0.1289

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