In this paper, we first introduce an n-dimensional star graph. Its topology is introduced and topological properties are derived. Then the properties are compared with the corresponding properties of a hypercube. The lower bound for the number of distinct paths for the star graph is derived using combinatorial analysis by introducing two special cases first. Two general formulas to determine the lower bound of the number of distinct paths between two arbitrary nodes are given later. With the formulas derived, we discuss the scenarios we didn't include in the formulas. Among other results, we determine the shortest path routing and disjoint paths. All these results confirm the already claimed topological superiority of the star graph over the hypercube.
Keywords: Cycles, Distinct Paths, Fault Tolerance, Interconnection Networks, Reliability, Star Graph.
|Commitee:||Englert, Burkhard, Maples, Tracy Bradley|
|School:||California State University, Long Beach|
|School Location:||United States -- California|
|Source:||MAI 52/01M(E), Masters Abstracts International|
|Subjects:||Applied Mathematics, Computer science|
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