Showing papers on "Dominating set published in 1975"
TL;DR: In this paper, the problem of finding disjoint dominating sets in a graph is studied, in particular, the domatic number d(G) of a graph G is defined as the maximum order of a partition of the vertices of G into dominating sets.
Abstract: Graph theoretic techniques provide a convenient tool for the investigation of communication networks. Here a communication network is represented by a nonoriented linear graph, in which the edges represent communication links and the vertices represent cities. A transmitting group is a set of cities which, acting as transmitting stations, can transmit messages to every city in the network. Stated graph theoretically, a transmitting group is a dominating set, i.e., a set of vertices D having the property that any vertex not in D is adjacent to at least one vertex in D . The problem of finding disjoint dominating sets in a graph is studied, in particular, the domatic number d(G) of a graph G is defined as the maximum order of a partition of the vertices of G into dominating sets.
52 citations
TL;DR: A limited number of research announcements may be communicated by each member of the Council who is also a member of a Society editorial committee as discussed by the authors, and manuscripts for research announcements should be sent directly to those members of the Publications Committees listed on the inside back cover.
Abstract: RESEARCH ANNOUNCEMENTS The purpose of this department is to provide early announcement of outstanding new results, with some indication of proof. Research announcements are limited to 100 typed lines of 65 spaces each. A limited number of research announcements may be communicated by each member of the Council who is also a member of a Society editorial committee. Manuscripts for research announcements should be sent directly to those members of the Publications Committees listed on the inside back cover.
8 citations