We show in this paper that the upper minus domination number −(G) of a claw-free cubic graph G is at most 1 2 |V (G)|. © 2006 Published by Elsevier B.V.

Let Y be a subset of real numbers. A Y dominating function of a graph G = (V, E) is a function f : V → Y such that u∈NG[v] f(u) ≥ 1 for all vertices v ∈ V , where NG[v] = {v} ∪ {u|(u, v) ∈ E}. Let f(S) = u∈S f(u) for any subset S of V and let f(V ) be the weight of f . The Y -domination problem is to find a Y -dominating function of minimum weight for a graph. In this paper, we study the variat...

In this paper, we give upper bounds on the upper signed domination number of [l, k] graphs, which generalize some results obtained in other papers. Further, good lower bounds are established for the minus ksubdomination number γ−101 ks and signed k-subdomination number γ −11 ks .

Given two graphs G1 and G2, the Kronecker product G1 ⊗G2 of G1 and G2 is a graph which has vertex set V (G1⊗G2) = V (G1)×V (G2) and edge set E(G1 ⊗ G2) = {(u1, v1)(u2, v2) : u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}. ∗ Research was partially supported by the National Nature Science Foundation of China (No. 11171207) and the Key Programs of Wuxi City College of Vocational Technology (WXCY2012-GZ-007). † Co...