Total domination and vertex-edge domination in trees.

Author
Y. B., Venkatakrishnan

Hari, Naresh Kumar

Chidambaram, Natarajan

Full text
https://www.revistaproyecciones.cl/article/view/3573
Abstract
A vertex v of a graph G = (V,E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set if every edge of E is ve-dominated by at least one vertex of S. The minimum cardinality of a vertex-edge dominating set of G is the vertex-edge domination number γve(G) . In this paper we prove (γt(T)−ℓ+1)/2 ≤ γve(T) ≤(γt(T)+ℓ−1)/2 and characterize trees attaining each of these bounds.
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