A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Arrangement graphs: a class of generalized star graphs
Information Processing Letters
The (n,k)-star graph: a generalized star graph
Information Processing Letters
Factoring N-cycles and counting maps of given genus
European Journal of Combinatorics
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
There is no optimal routing policy for the torus
Information Processing Letters
Transposition Networks as a Class of Fault-Tolerant Robust Networks
IEEE Transactions on Computers
Higher dimensional hexagonal networks
Journal of Parallel and Distributed Computing
On the number of factorizations of a full cycle
Journal of Combinatorial Theory Series A
On the surface area of the (n,k)-star graph
Theoretical Computer Science
Distance formula and shortest paths for the (n,k)-star graphs
Information Sciences: an International Journal
The number of shortest paths in the arrangement graph
Information Sciences: an International Journal
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We enumerate all of the shortest paths between any vertex υ and the identity vertex in an (n, k)-star graph by enumerating the minimum factorizations of υ in terms of the transpositions corresponding to edges in that graph. This result generalizes a previous one for the star graph, and can be applied to obtain the number of the shortest paths between a pair of vertices in some of the other similar structures. It also implies an algorithm to enumerate all such paths.