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Total domination in graphs

✍ Scribed by E. J. Cockayne; R. M. Dawes; S. T. Hedetniemi


Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
374 KB
Volume
10
Category
Article
ISSN
0028-3045

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πŸ“œ SIMILAR VOLUMES


Upper total domination in claw-free grap
✍ Odile Favaron; Michael A. Henning πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 114 KB

## Abstract A set __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__ (other than itself). The maximum cardinality of a minimal total dominating set of __G__ is the upper total domination number of __G__, denoted by Ξ“~__

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✍ Favaron, Odile; Henning, Michael A.; Mynhart, Christina M.; Puech, JoοΏ½l πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 132 KB πŸ‘ 3 views

A set S of vertices of a graph G is a total dominating set, if every vertex of V (G) is adjacent to some vertex in S. The total domination number of G, denoted by Ξ³ t (G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at leas

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In a graph G Γ… (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then ''domination'' requires every vertex to be protected. Thus, S ʚ V (G) is a dominating set if ʜ s √ S N[s] Γ… V (G). For total domination, eac

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## Abstract Let __G__ = (__V, E__) be a connected graph. A set __D__ βŠ‚ __V__ is a __set‐dominating set__ (sd‐set) if for every set __T__ βŠ‚ __V__ βˆ’ __D__, there exists a nonempty set __S__ βŠ‚ __D__ such that the subgraph γ€ˆ__S__ βˆͺ __T__〉 induced by __S__ βˆͺ __T__ is connected. The set‐domination number

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✍ Michael A. Henning; Anders Yeo πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 272 KB πŸ‘ 1 views

## Abstract A set __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__. The minimum cardinality of a total dominating set of __G__ is the total domination number Ξ³~t~(__G__) of __G__. It is known [J Graph Theory 35 (2000)