Abstract:In this paper, we introduce the notion of the weak majority dimension of a digraph which is well-defined for any digraph. We first study properties shared by the weak dimension of a digraph and show that a weak majority dimension of a digraph can be arbitrarily large. Then we present a complete characterization of digraphs of weak majority dimension 0 and 1, respectively, and show that every digraph with weak majority dimension at most two is transitive. Finally, we compute the weak majority dimensions of dire… Show more
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