Signed total domination number of a graph
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Date
2001
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Technická Univerzita v Liberci
Technical university of Liberec, Czech Republic
Technical university of Liberec, Czech Republic
Abstract
The signed total domination number of a graph is a certain variant of the domination number. If v is a vertex of a graph G, then N(v) is its oper neighbourhood, i.e. the set of all vertices adjacent to v 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 ∑x∈N(v) f(x) ≥ 1 for each v ∈ V(G). The minimum of values ∑x∈V(G) f(x), taken over all STDF's of G, is called the signed total domination number of G and denoted by γst(G). A theorem stating lower bounds for γst(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 γst(G) is not bounded from below in general.
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Subject(s)
cartesian product of graphs, circuit, complete bipartite graph, complete graph, regular graph, signed total dominating function, signed total domination number
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ISSN
0011-4642