Hua-ming Xing

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Let G = (V, E) be a graph. A function f : V → {−1,+1} defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, γ t (G), is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total(More)
Let G = (V,E) be a simple graph. A set D ⊆ V is a dominating set of G if every vertex of V − D is adjacent to a vertex of D. The domination number of G, denoted by γ(G), is the minimum cardinality of a dominating set of G. We prove that if G is a Hamiltonian graph of order n with minimum degree at least six, then γ(G) ≤ 6n 17 .
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