| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 91 ===
Given a graph and a vertex v belong to V (G) who knows a message s. Suppose we
want to give a series of calls to transmit the message to all the vertices in G with
the following constraints :
(1) u can transmit the message s to w only if u knows the message s;
(2) a vertex can only call an adjacent vertex; and
(3) a vertex can participate in only one call per unit of time.
If each call requires one unit of time, the problem is to find the minimum value of time to complete the transmission. Such a minimum value of a graph G with respect to v is denoted by b(G, v), and the broadcasting time of G, denoted by b(G), is defined by b(G) =min{b(G, v) | v blong to V (G)}.
We study a more general problem which we called the Multi-messages, Multi-originator broadcasting problem, in this thesis. Given a graph G, m messages 1,2, · · · , m, and a set S include to V (G) such that each v in S knows all the messages. The (S; m)-broadcasting number of G with respect to C, denoted by tC(G; S; m), is the number of time needed to complete the broadcasting from S under the calling
scheme C. The(S; m)-broadcasting number of G, denoted by t(G; S; m), is defined by t(G; S; m) = min{t_{C}(G; S; m) | C is a calling scheme}. And we define the (k; m)-broadcasting number of G to be the number t(G; k; m) = min{t(G; S; m) | S include to V (G), |S| = k}.
We study the (k; m)-broadcasting number of some calsses of graphs in this thesis.We consider the (k; m)-broadcasting numbers of complete bipartite graphs,and use it to find the (1; m)-broadcasting numbers of complete graphs. We also
study the (S; m)-broadcasting numbers of paths and cycles, and discuss the (k; m)-broadcasting numbers of these two kinds of graphs.
key word : broadcasting in graph
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