p. 19 - 28 Signed star (j, k)-domatic number of a graph S. M. Sheikholeslami and L. Volkmann Received: September 4, 2012; Accepted: May October 25, 20013 Abstract. Let G be a simple graph without isolated vertices with edge set E(G), and let j and k be two positive integers. A function f : E(G) \to {-1, 1} is said to be a signed star j-dominating function on G if \sum_{e \in E(v)} f(e) >= j for every vertex v of G, where E(v)= {uv \in E(G) ; u \in N(v)}. A set {f1, f2, . . . ,fd} of distinct signed star k-dominating functions on G with the property that $\sum_{i=1}^{d} fi(e) <= k for each e \in E(G), is called a signed star (j, k)-dominating family (of functions) on G. The maximum number of functions in a signed star (j, k)-dominating family on G is the signed star (j, k)-domatic number of G, denoted by d^{(j, k)}_{SS}(G).
In this paper we study properties of the signed star
(j, k)-domatic number of a graph G. In particular, we
determine bounds on d^{(j, k)}_{SS}(G). Some of our results
extend these one given by Atapour, Sheikholeslami, Ghameslou and
Volkmann for the signed star domatic number,
Sheikholeslami and Volkmann for the signed star
(k, k)-domatic number and Sheikholeslami and Volkmann
for the signed star k-domatic number.
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