The Strong (Weak) Vv-Dominating Set of a Graph

Abstract

Two vertices , ∈ vv-dominate each other if they incident on the same block. A vertex ∈ strongly vv-dominates a vertex ∈ if u and w, vv-dominate each other and () ≥ (). 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 () is the order of the minimum strong vv-dominating set of G. Similarly weak vvdomination number γ () 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.

Resolving Domination Number pada Keluarga Graf Buku

“…Resolving domination number adalah Kardinalitas minimum dari resolving dominating set [1]. Resolving dominating set merupakan himpunan titik pembeda yang mendominasi, artinya titik titik pada resolving dominating set harus mendominasi titik-titik disekitarnya, minimun, dan setiap titik memiliki representasi yang berbeda [2]. Misalkan W = {w 1 , w 2 , ..., w i } adalah himpunan titik yang mendominasi titik-titik lainnya yang bukan anggota W , dan semua titik memiliki representasi yang berbeda, maka W disebut resolving dominating set.…”