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

Authors

DOI:

https://doi.org/10.23755/rm.v48i0.1211

Keywords:

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

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.

Author Biographies

  • A Jancy Vini, Holy Cross College, Nagercoil
    Mathematics
  • C Jayasekaran, Pioneer Kumaraswmy College, Nagercoil
    Mathematics

References

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

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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