Total domination and vertex-edge domination in trees.

• Y. B., Venkatakrishnan ^[1] ; Hari, Naresh Kumar ^[1] ; Chidambaram, Natarajan ^[1]
  1. [1] SASTRA Deemed University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 2, 2019, págs. 295-304
• Idioma: inglés
• DOI: 10.4067/s0716-09172019000200295
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• Resumen

  • 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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