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Abstract

A set S ⊆ V is said to be a relatively prime detour dominating set of a graph G if it has at least two members is a detour set and a dominating set for any pair of vertices b and w such that (deg(b), deg(w)) = 1. The lowest cardinality of a relatively prime detour dominating set is indicated by γrpdn (G) and defines the lowest cardinality of a relatively prime detour dominating set of order γrpdn (G) said to as a γrpdn-set of G. If there is no relatively prime detour dominating set, the relatively prime detour domination number is zero. In this paper, the idea of switching graphs and providing some conclusions on the relatively prime detour domination number for path graphs, star graphs, bistar graphs, cycle graphs and various standard graphs are probed. This paper could be framed from the terms from the abundant epitome of domination graphs. The speculations are explicated with legitimate illustrations. The proof strategy is given lucidly, and the assessment of finding the detour set, domination set and degree of the vertices are stated plainly. Graph domination is wielded plenty in numerous areas and also we begin research on the concept of relatively prime detour domination number for switching graphs. The difficulty of relatively prime detour domination number is examined for us we starts a study on this idea of relatively prime detour domination number for switching graph.

Keywords

Detour number, Detour domination number, Domination number, Relatively prime detour domination number, Relatively prime domination number and switching

Subject Area

Mathematics

Article Type

Article

First Page

711

Last Page

719

Creative Commons License

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

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