### 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 d_{vv}(u) ≥ d_{vv}(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 γ_{svv}(G) is the order of the minimum strong vv-dominating set of G. Similarly weak vv-domination number γ_{wvv}(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 language | English |
---|---|

Pages (from-to) | 24-33 |

Number of pages | 10 |

Journal | Malaysian Journal of Science |

Volume | 38 |

Issue number | 3 |

DOIs | |

Publication status | Published - 01-01-2019 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

*Malaysian Journal of Science*,

*38*(3), 24-33. https://doi.org/10.22452/mjs.vol38no3.3

}

*Malaysian Journal of Science*, vol. 38, no. 3, pp. 24-33. https://doi.org/10.22452/mjs.vol38no3.3

**Strong (weak) VV-dominating set of a graph.** / Udupa, Sayinath; Bhat, R. S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong (weak) VV-dominating set of a graph

AU - Udupa, Sayinath

AU - Bhat, R. S.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85077027030&partnerID=8YFLogxK

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U2 - 10.22452/mjs.vol38no3.3

DO - 10.22452/mjs.vol38no3.3

M3 - Article

AN - SCOPUS:85077027030

VL - 38

SP - 24

EP - 33

JO - Malaysian Journal of Science

JF - Malaysian Journal of Science

SN - 1394-3065

IS - 3

ER -