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Domination parameters of a graph with added vertex

100%

Zwierzchowski M.

tom Vol. 24, no. 2

231-234

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.

Selected problems of technological preparation of production of a two-segment passenger inland waterways ship of a combined structure

88%

Górski Z. , Pyszko R.

2006

tom S 2

91-96

This paper presents some aspects of technical preparation of production of inland waterways ship of combined structure contained partly: classical structures (bow and stern part) and sandwich panel structure. Due to prototype character of inland waterways ship structure it was decided to define a new subdivision of shipbuilding process into phases and create new classification principles if constructional and technological documentations.