Matchings and total domination subdivision number in graphs with few induced 4-cycles

• Autorzy: Odile Favaron , Hossein Karami , Rana Khoeilar , Seyed Mahmoud Sheikholeslami
• Języki publikacji: EN

Abstrakty

EN

A set S of vertices of a graph G = (V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γₜ(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $sd_{γₜ(G)}$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Favaron, Karami, Khoeilar and Sheikholeslami (Journal of Combinatorial Optimization, to appear) conjectured that: For any connected graph G of order n ≥ 3, $sd_{γₜ(G)} ≤ γₜ(G)+1$. In this paper we use matchings to prove this conjecture for graphs with at most three induced 4-cycles through each vertex.

Słowa kluczowe

EN

matching; barrier; total domination number; total domination subdivision number

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 4
• Strony: 611-618

Daty

wydano

2010

otrzymano

2009-09-24

poprawiono

2010-01-07

zaakceptowano

2010-01-07

Twórcy

autor

Odile Favaron

• Univ Paris-Sud, LRI, UMR 8623, Orsay, F-91405, France, CNRS, Orsay, F-91405

autor

Hossein Karami

• Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran

autor

Rana Khoeilar

• Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran

autor

Seyed Mahmoud Sheikholeslami

• Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1517