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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Preeti B. Jinagouda
Department of Mathematics, SDMCET, Dharwad, Karnataka, India
Electrical & Electronics Engineering

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Degree equitable restrained double domination in graphs Sunilkumar M Hosamani; Shailaja Shirkol; Preeti B. Jinagouda; Marcin Krzywkowski
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.1.10

Abstract

A subset D ⊆ V(G) is called an equitable dominating set of a graph G if every vertex v ∈ V(G) \ D has a neighbor u ∈ D such that |dG(u)-dG(v)| ≤ 1. An equitable dominating set D is a degree equitable restrained double dominating set (DERD-dominating set) of G if every vertex of G is dominated by at least two vertices of D, and 〈V(G) \ D〉 has no isolated vertices. The DERD-domination number of G, denoted by γcl^e(G), is the minimum cardinality of a DERD-dominating set of G. We initiate the study of DERD-domination in graphs and we obtain some sharp bounds. Finally, we show that the decision problem for determining γcl^e(G) is NP-complete.
Co-Authors Marcin Krzywkowski Shailaja Shirkol Sunilkumar M Hosamani