The outer-connected vertex edge domination number in Cartesian product graphs

Akwu, Abolape Deborah; Oyewumi, Opeyemi; Ajayi, Deborah Olayide

doi:10.1080/09720529.2020.1748272

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“…A subset D of V(G) is an outer-connected vertex-edge dominating set (OCVEDS) of G if D is a vertex edge dominating set of G and the graph G \ D is connected. The outer connected vertex-edge domination number of a graph G, denoted by γ oc ve (G), is the minimum cardinality of an outer connected vertex edge dominating set of G. The outer connected vertex edge domination number in Cartesian product of graphs has been given in [10].…”

Section: Introductionmentioning

confidence: 99%

The outer-connected vertex edge domination number in Lexicographic product graphs

Oyewumi¹,

Akwu²,

Ben³

2019

Open J. Discret. Appl. Math.

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An outer-connected vertex edge dominating set (OCVEDS) for an arbitrary graph G is a set D ⊂ V(G) such that D is a vertex edge dominating set and the graph G \ D is connected. The outer-connected vertex edge domination number of G is the cardinality of a minimum OCVEDS of G, denoted by γ oc ve (G). In this paper, we give the outer-connected vertex edge dominating set in lexicographic product of graphs.

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Section: Introductionmentioning

confidence: 99%