Total domination and vertex-edge domination in tres

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...

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Autores principales:	Venkatakrishnan,Y. B., Kumar,H. Naresh, Natarajan,C.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Vertex-edge dominating set total dominating set trees
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200295
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spelling	oai:scielo:S0716-091720190002002952019-05-30Total domination and vertex-edge domination in tresVenkatakrishnan,Y. B.Kumar,H. NareshNatarajan,C. Vertex-edge dominating set total dominating set trees 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.2 20192019-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200295en10.4067/S0716-09172019000200295
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Vertex-edge dominating set total dominating set trees
spellingShingle	Vertex-edge dominating set total dominating set trees Venkatakrishnan,Y. B. Kumar,H. Naresh Natarajan,C. Total domination and vertex-edge domination in tres
description	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.
author	Venkatakrishnan,Y. B. Kumar,H. Naresh Natarajan,C.
author_facet	Venkatakrishnan,Y. B. Kumar,H. Naresh Natarajan,C.
author_sort	Venkatakrishnan,Y. B.
title	Total domination and vertex-edge domination in tres
title_short	Total domination and vertex-edge domination in tres
title_full	Total domination and vertex-edge domination in tres
title_fullStr	Total domination and vertex-edge domination in tres
title_full_unstemmed	Total domination and vertex-edge domination in tres
title_sort	total domination and vertex-edge domination in tres
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000200295
work_keys_str_mv	AT venkatakrishnanyb totaldominationandvertexedgedominationintres AT kumarhnaresh totaldominationandvertexedgedominationintres AT natarajanc totaldominationandvertexedgedominationintres
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Total domination and vertex-edge domination in tres

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