The signed domatic number of some regular graphs

Authors:
Dirk Meierling;Lutz Volkmann;Stephan Zitzen
Affiliations:
Lehrstuhl II für Mathematik, RWTH-Aachen University, 52056 Aachen, Germany;Lehrstuhl II für Mathematik, RWTH-Aachen University, 52056 Aachen, Germany;Lehrstuhl II für Mathematik, RWTH-Aachen University, 52056 Aachen, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

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 @?"x"@?"N"["v"]f(x)=1 for each v@?V(G), where N[v] is the closed neighborhood of v, then f is a signed dominating function on G. A set {f"1,f"2,...,f"d} of signed dominating functions on G with the property that @?"i"="1^df"i(x)@?1 for each x@?V(G), is called a signed dominating family (of functions) on G. The maximum number of functions in a signed dominating family on G is the signed domatic number on G. In this paper, we investigate the signed domatic number of some circulant graphs and of the torus C"pxC"q.