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Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs

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Volkmann L.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 4

641-650

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 Σx∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that Σdi=1 fi(x) ≤ k for each x ∈ V (G), is called a signed total (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed total (k, k)-dominating family on G is the signed total (k, k)-domatic number of G. In this article we mainly present upper bounds on the signed total (k, k)- domatic number, in particular for regular graphs.

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1 Discussiones Mathematicae Graph Theory

1 Volkmann L.

1 2015

Wyniki wyszukiwania

Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs