| Summary: | 碩士 === 國立交通大學 === 應用數學系 === 88 === Broadcasting from an originator is the process of passing one unit of information from that source to every other vertex in a connected graph G=(V, E). This is accomplished by a series of calls over the edges of G, subject to the following constraints：(1) each call requires one unit of times；(2) a vertex can only call an adjacent vertex；and (3) a vertex can participate in only one call per unit of time. We mainly discuss the following three problems：(1) finding the broadcast number b(u) of a vertex u which is the minimum number if calls needed to broadcast the information to all other vertices；(2) computing the broadcast number of G, denoted by b(G), which is the minimum broadcast number of a vertex in G；(3) determining the broadcast center of G, denoted by BC(G), which is the set of all vertices having minimum broadcast number. In this thesis, we simplify Slater, Cockayne and Hedetniemi's algorithm for finding the broadcast center BC(T) of a tree T by using a labeling algorithm. We also study the problem of broadcasting messages with multiple originators for paths, cycles, full m-ary trees, complete graphs, and complete bipartite graphs.
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