Strong (weak) VV-dominating set of a graph
Malaysian Journal of Science
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 (u) ≥ d (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 (G) is the order of the minimum strong vv-dominating set of G. Similarly weak vv-domination number γ (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. vv vv svv wvv
Udupa, Sayinath and Bhat, R. S., "Strong (weak) VV-dominating set of a graph" (2019). Open Access Archive. 794.