Signed reinforcement numbers of certain graphs∗
نویسندگان
چکیده
Let G be a graph with vertex set V (G). A function f : V (G) → {−1, 1} is a signed dominating function of G if, for each vertex of G, the sum of the values of its neighbors and itself is positive. The signed domination number of a graph G, denoted γs(G), is the minimum value of ∑ v∈V (G) f(v) over all the signed dominating functions f of G. The signed reinforcement number of G, denoted Rs(G), is defined to be the minimum cardinality |S| of a set S of edges such that γs(G+S) < γs(G). In this paper, we initialize the study of signed reinforcement number and determine the exact values of Rs(G) for several classes of graphs.
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