Signed Total Domination Nnumber of a Graph |
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Authors: | Bohdan Zelinka |
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Institution: | (1) katedra aplikovane matematiky, Technicka universita, Voronezska 13, 461 17 Liberec, Czech Republic |
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Abstract: | The signed total domination number of a graph is a certain variant of the domination number. If is a vertex of a graph G, then N() is its oper neighbourhood, i.e. the set of all vertices adjacent to in G. A mapping f: V(G)-1, 1, where V(G) is the vertex set of G, is called a signed total dominating function (STDF) on G, if
for each
V(G). The minimum of values
, taken over all STDF's of G, is called the signed total domination number of G and denoted by st(G). A theorem stating lower bounds for st(G) is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on n-side prisms. At the end it is proved that st(G) is not bounded from below in general. |
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Keywords: | signed total dominating function signed total domination number regular graph circuit complete graph complete bipartite graph Cartesian product of graphs |
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