Signed (k, k)-domatic number of a graph
نویسندگان
چکیده
Let G be a finite and simple graph with vertex set V (G), and let f: V (G)→ {−1, 1} be a two-valued function. If k > 1 is an integer and ∑ x∈N[v] f(x) > k for each v ∈ V (G), where N [v] is the closed neighborhood of v, then f is a signed k-dominating function on G. A set {f1, f2, . . . , fd} of signed kdominating functions on G with the property that ∑ d i=1 fi(x) 6 k for each x ∈ V (G), is called a signed (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed (k, k)-dominating family on G is the signed (k, k)-domatic number on G, denoted by dkS(G). In this paper we initiate the study of the signed (k, k)-domatic number, and we present different bounds on dkS(G). Some of our results are extensions of well-known properties of the signed domatic number dS(G) = d 1 S(G).
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