The signed domatic number of some regular graphs

Abstract: Let be a finite and simple graph with vertex set , and let be a two-valued function. If for each , where is the closed neighborhood of , then is a signed dominating function on . A set of signed dominating functions on with the property that for each , is called a signed dominating family (of functions) on . The maximum number of functions in a signed dominating family on is the signed domatic number on . In this paper, we investigate the signed domatic number of some circulant graphs and of the torus . [Copyright &y& Elsevier]