Upper bounds on the signed (k, k)-domatic number |
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Authors: | Lutz Volkmann |
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Institution: | 1. Lehrstuhl II für Mathematik, RWTH-Aachen University, 52056, Aachen, Germany
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Abstract: | Let G be a 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 ${\sum_{x\in Nv]} f(x) \ge k}$ for each ${v \in V(G)}$ , where Nv] is the closed neighborhood of v, then f is a signed k-dominating function on G. A set {f 1,f 2, . . . ,f d } of distinct signed k-dominating functions on G with the property that ${\sum_{i=1}^d f_i(x) \le k}$ for each ${x \in V(G)}$ , 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 of G. In this article we mainly present upper bounds on the signed (k, k)-domatic number, in particular for regular graphs. |
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