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Proof of a conjecture in domination theory

https://doi.org/10.1016/S0012-365X(93)E0231-RGet rights and content
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Abstract

A dominating set D of a graph G is a least dominating set (l.d.s) if γ(〈D〉) ⩽ γ(〈D1〉) for any dominating set D1 (γ denotes domination number). The least domination number γ1(G) of G is the minimum cardinality of a l.d.s. We prove a conjecture of Sampathkumar (1990) that γ13p5 for any connected graph G of order p ⩾ 2.

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