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Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping every person in the network knows a unique item of information and needs to communicate it to everyone else. In broadcasting one individual has an item of information which needs to be communicated to everyone else. We review the results that have been obtained on these and related problems.

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A set D of vertices of a finite, undirected graph C = ( V , E) is a total dominating set if every vertex of Y is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number of C (the largest order of a partition of C into total dominating sets).

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