Global neighbourhood domination
A subset D of vertices of a graph G is called a global neighbourhood dominating set(gnd - set) if D is a dominating set for both G and G N, where G N is the neighbourhood graph of G. The global neighbourhood domination number(gnd - number) is the minimum cardinality of a global neigh...
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| Autores principales: | , |
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| Lenguaje: | Spanish / Castilian |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2014
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000100003 |
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| Sumario: | A subset D of vertices of a graph G is called a global neighbourhood dominating set(gnd - set) if D is a dominating set for both G and G N, where G N is the neighbourhood graph of G. The global neighbourhood domination number(gnd - number) is the minimum cardinality of a global neighbourhood dominating set of G and is denoted by γ gn(G). In this paper sharp bounds for γ gn, are supplied for graphs whose girth is greater than three. Exact values ofthis number for paths and cycles are presented as well. The characterization result for a subset ofthe vertex set of G to be a global neighbourhood dominating set for G is given and also characterized the graphs of order n having gnd -numbers 1, 2, n — 1,n — 2, n. |
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