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On the signed total domatic number of a graph. (English) Zbl 1164.05421

Summary: In this paper, we define the signed total domatic number of a graph in an analogous way to that of the fractional domatic number defined by D.F.Rall [Congr.Numerantium 74, 100-106 (1990; Zbl 0691.05044)]. A function \(f\:V(G)\to \{-1,1\}\) defined on the vertices of a graph \(G\) is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. A set \(\{f_1, \dots ,f_d\}\) of signed total dominating functions on \(G\) such that \(\sum _{i=1}^df_i(v)\leq 1\) for each vertex \(v\in V(G)\) is called a signed total dominating family of functions on \(G\). The signed total domatic number of \(G\) is the maximum number of functions in a signed total dominating family of \(G\). In this paper we investigate the signed total domatic number for special classes of graphs.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)

Citations:

Zbl 0691.05044
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