A linear time algorithm for minimum equitable dominating set in trees
Abstract Let G = (V, E) be a graph. A subset D e of V is said to be an equitable dominating set if for every v ∈ V \ D e there exists u ∈ D e such that uv ∈ E and |deg(u) − deg(v)| ≤ 1, where, deg(u) and deg(v) denote the degree of the vertices u...
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| Auteurs principaux: | , |
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| Langue: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2021
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| Accès en ligne: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400805 |
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| Résumé: | Abstract Let G = (V, E) be a graph. A subset D e of V is said to be an equitable dominating set if for every v ∈ V \ D e there exists u ∈ D e such that uv ∈ E and |deg(u) − deg(v)| ≤ 1, where, deg(u) and deg(v) denote the degree of the vertices u and v respectively. An equitable dominating set with minimum cardinality is called the minimum equitable dominating set and its cardinality is called the equitable domination number and it is denoted by γ e . The problem of finding minimum equitable dominating set in general graphs is NP-complete. In this paper, we give a linear time algorithm to determine minimum equitable dominating set of a tree. |
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