Strong (weak) VV-dominating set of a graph

Sayinath Udupa, R. S. Bhat

Research output: Contribution to journalArticle

Abstract

Two vertices u, w ∈ V vv-dominate each other if they incident on the same block. A vertex u ∈ V strongly vv-dominates a vertex w ∈ V if u and w, vv-dominate each other and dvv(u) ≥ dvv(w). A set of vertices is said to be strong vv-dominating set if each vertex outside the set is strongly vv-dominated by at least one vertex inside the set. The strong vv-domination number γsvv(G) is the order of the minimum strong vv-dominating set of G. Similarly weak vv-domination number γwvv(G) is defined. We investigate some relationship between these parameters and obtain Gallai’s theorem type results. Several upper and lower bounds are established. In addition, we characterize the graphs attaining some of these bounds.

Original languageEnglish
Pages (from-to)24-33
Number of pages10
JournalMalaysian Journal of Science
Volume38
Issue number3
DOIs
Publication statusPublished - 01-01-2019

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Dominating Set
Domination number
Graph in graph theory
Vertex of a graph
Upper and Lower Bounds
Theorem

All Science Journal Classification (ASJC) codes

  • General

Cite this

Udupa, Sayinath ; Bhat, R. S. / Strong (weak) VV-dominating set of a graph. In: Malaysian Journal of Science. 2019 ; Vol. 38, No. 3. pp. 24-33.
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Strong (weak) VV-dominating set of a graph. / Udupa, Sayinath; Bhat, R. S.

In: Malaysian Journal of Science, Vol. 38, No. 3, 01.01.2019, p. 24-33.

Research output: Contribution to journalArticle

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