Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
The numbers of spanning trees of the cubic cycle C3N and the quadruple cycle C4N
Discrete Mathematics
Hamiltonian cycles in circulant digraphs with two stripes
Discrete Mathematics
Counting structures in the Mo¨bius ladder
Discrete Mathematics
The number of spanning trees in circulant graphs
Discrete Mathematics
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
A survey on multi-loop networks
Theoretical Computer Science
Unhooking circulant graphs: a combinatorial method for counting spanning trees and other parameters
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Hi-index | 0.00 |
Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies It has long been known that the number of spanning trees in n-node circulant graphs with constant jumps satisfies a recurrence relation in n For the non-constant-jump case, i.e., where some jump sizes can be functions of the graph size, only a few special cases such as the Möbius ladder had been studied but no general results were known. In this note we show how that the number of spanning trees for all classes of n node circulant graphs satisfies a recurrence relation in n even when the jumps are non-constant (but linear) in the graph size The technique developed is very general and can be used to show that many other structures of these circulant graphs, e.g., number of Hamiltonian Cycles, Eulerian Cycles, Eulerian Orientations, etc., also satisfy recurrence relations. The technique presented for deriving the recurrence relations is very mechanical and, for circulant graphs with small jump parameters, can easily be quickly implemented on a computer We illustrate this by deriving recurrence relations counting all of the structures listed above for various circulant graphs.