Diameter and Connectivity Considerations in the Design of Communication Networks
CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE
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A communication network is modeled by an undirected graph without loops and multiple edges. The maximal message delay index, in the network, is expressed in terms of the diameter of the graph. Three reliability measures are considered a given minimal degree, edge-connectivity and vertex connectivity. Let H1k,d be the class of all graphs with diameter d and minimal degree k, H2k,d is a subclass of H2k,d consisting of all k-edge connected graphs in H1k,d and H3k,d is the subclass of all K-vertex connected graphs in H2k,d. Hin,k,d consists of the graphs in Hik,d with exactly n vertices i1,2,3. Let fik,d, gik,d be the minimum number of vertices and edges, respectively, that an Hik,d- graph must have and let gin,k,d be the minimal number of edges of an Hin,k,d-graph i1,2,3. In Chapter 2 and 3 our main concern is to calculate the values of fik,d, gik,d and gin,k,d for arbitrary natural numbers n,k,d i1,2,3. Furthermore, graphs attaining the minimal number of vertices and edges are constructed.
- Numerical Mathematics
- Computer Systems
- Non-Radio Communications