We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σ p 2. In the case of linear matroids, which are represented over pol...
A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all t...
Alice Devillers, Michael Giudici, Cai Heng Li, Che...
It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers conne...
Edward Dobson, Heather Gavlas, Joy Morris, Dave Wi...
Let G be a graph. A vertex labeling of G is distinguishing if the only label-preserving automorphism of G is the identity map. The distinguishing number of G, D(G), is the minimum...
We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the trans...