Domination parameters of a graph with added vertex

• Autorzy: Zwierzchowski M.
• Języki publikacji: EN

Abstrakty

EN

Let G = (V, E) be a graph. A subset D ⊆ V is a total dominating set of G if for every vertex y ∈ V there is a vertex x ∈ D with xy ∈ E. A subset D ⊆ V is a strong dominating set of G if for every vertex y ∈ V - D there is a vertex x ∈ D with xy &isin E and degG(x) ≥ degG(y). The total domination number γt(G) (the strong domination number γS(G)) is defined as the minimum cardinality of a total dominating set (a strong dominating set) of G. The concept of total domination was first defined by Cockayne, Dawes and Hedetniemi in 1980 [1], while the strong domination was introduced by Sampathkumar and Pushpa Latha in 1996 [3]. By a subdivision of an edge uv ∈ E we mean removing edge uv, adding a new vertex x, and adding edges ux and vx. A graph obtained from G by subdivision an edge uv ∈ E is denoted by G ⊕ uxvx. The behaviour of the total domination number and the strong domination number of a graph G ⊕ uxvx is developed.

Słowa kluczowe

EN

total domination number; strong domination number; subdivision

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 2
• Strony: 231--234
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Zwierzchowski M.

• Technical University of Szczecin, Institute of Mathematics, al. Piastów 48/49, 70-310 Szczecin, Poland,

Bibliografia

• [1] Cockayne E. J., Dawes R. M., Hedetniemi S.T.: Total domination in graphs. Networks 10 (1980), 211-219.
• [2] Hedetniemi S.T., Laskar R. C: Bibliography on domination in graphs and some basic definitions of domination parameters. Discrete Mathematics 86 (1990), 257—277.
• [3] Pushpa Latha L., Sampathkumar E.: Strong weak domination and domination balance in a graph. Discrete Mathematics 161 (1996), 235-242.