Flows that are sums of hamiltonian cycles in Cayley graphs on abelian groups

Flows that are sums of hamiltonian cycles in Cayley graphs on abelian groups

If X is any connected Cayley graph on any finite abelian group, we determine precisely which flows on X can be written as a sum of hamiltonian cycles. (This answers a question of B. Alspach.) In particular, if the degree of X is at least 5, and X has an even number of vertices, then the flows that can be so written are precisely the even flows, that is, the flows f , such that ∑ α∈E(X) f(α) is ...

Flows that are sums of hamiltonian cycles in abelian Cayley graphs

If X is any connected Cayley graph on any finite abelian group, we determine precisely which flows on X can be written as a sum of hamiltonian cycles. In particular, if the degree of X is at least 5, and X has an even number of vertices, then it is precisely the even flows, that is, the flows f , such that ∑ α∈E(X) f(α) is divisible by 2. On the other hand, there are infinitely many examples of...

On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

Nowhere-zero 3-flows in Cayley Graphs of Abelian Groups

NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS

Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.