On Independent Transversal Dominating Sets in Graphs

Authors

  • Daven Sapitanan Sevilleno
  • Ferdinand P. Jamil

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3904

Keywords:

Independent transversal dominating set, Independent transversal total dominating set, Independent transversal domination number, Independent transversal total domination number

Abstract

A set S ⊆ V (G) is an independent transversal dominating set of a graph G if S is a dominating set of G and intersects every maximum independent set of G. An independent transversal dominating set which is a total dominating set is an independent transversal total dominating set. The minimum cardinality γit(G) (resp. γitt(G)) of an independent transversal dominating set (resp. independent transversal total dominating set) of G is the independent transversal domination number (resp. independent transversal total domination number) of G. In this paper, we show that for every positive integers a and b with 5 ≤ a ≤ b ≤ 2a − 2, there exists a connected graph G for which γit(G) = a and γitt(G) = b. We also study these two concepts in graphs which are the join, corona or composition of graphs.

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Published

2021-01-31

Issue

Vol. 14 No. 1: (January 2021)

Section

Nonlinear Analysis

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How to Cite

On Independent Transversal Dominating Sets in Graphs. (2021). European Journal of Pure and Applied Mathematics, 14(1), 149-163. https://doi.org/10.29020/nybg.ejpam.v14i1.3904