An upper bound on the total outer-independent domination number of a tree

• Autorzy: Krzywkowski M.
• Języki publikacji: EN

Abstrakty

EN

A total outer-independent dominating set of a graph G = (V (G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent. The total outer-independent domination number of a graph G, denoted by [formula], is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n ≥ 4, with l leaves and s support vertices we have [formula], and we characterize the trees attaining this upper bound.

Słowa kluczowe

EN

total outer-independent domination; total domination; tree

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 1
• Strony: 153--158
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Krzywkowski M.

• Gdansk University of Technology Faculty of Electronics, Telecommunications and Informatics ul. Narutowicza 11/12, 80-233 Gdansk, Poland,

Bibliografia

• [1] M. Chellali, T. Haynes, Total and paired-domination numbers of a tree, AKCE Int. J. Graphs Comb. 1 (2004), 69–75.
• [2] E. Cockayne, R. Dawes, S. Hedetniemi, Total domination in graphs, Networks 10 (1980), 211–219.
• [3] T. Haynes, S. Hedetniemi, P. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
• [4] T. Haynes, S. Hedetniemi, P. Slater (eds.), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.
• [5] M. Krzywkowski, Total outer-independent domination in graphs, submitted.