Distance domination versus iterated domination

Gábor Bacsó, Z. Tuza

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A k-dominating set in a graph G is a set S of vertices such that every vertex of G is at distance at most k from some vertex of S. Given a class D of finite simple graphs closed under connected induced subgraphs, we completely characterize those graphs G in which every connected induced subgraph has a connected k-dominating subgraph isomorphic to some D∈D. We apply this result to prove that the class of graphs hereditarily D-dominated within distance k is the same as the one obtained by iteratively taking the class of graphs hereditarily dominated by the previous class in the iteration chain. This strong relation does not remain valid if the initial hereditary restriction on D is dropped.

Original language English 2672-2675 4 Discrete Mathematics 312 17 https://doi.org/10.1016/j.disc.2011.12.008 Published - Sep 6 2012

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Domination
Induced Subgraph
Graph in graph theory
Finite Graph
Dominating Set
Vertex of a graph
Simple Graph
Subgraph
Isomorphic
Valid
Restriction
Iteration
Closed
Class

Keywords

• Class of connected graphs
• Distance domination
• Dominating set
• Forbidden induced subgraph

ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

Cite this

In: Discrete Mathematics, Vol. 312, No. 17, 06.09.2012, p. 2672-2675.

Research output: Contribution to journalArticle

Bacsó, Gábor ; Tuza, Z. / Distance domination versus iterated domination. In: Discrete Mathematics. 2012 ; Vol. 312, No. 17. pp. 2672-2675.
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