2 research outputs found
Stability of circulant graphs
The canonical double cover of a graph is the
direct product of and . If
then
is called stable; otherwise is called unstable. An unstable
graph is nontrivially unstable if it is connected, non-bipartite and distinct
vertices have different neighborhoods. In this paper we prove that every
circulant graph of odd prime order is stable and there is no arc-transitive
nontrivially unstable circulant graph. The latter answers a question of Wilson
in 2008. We also give infinitely many counterexamples to a conjecture of
Maru\v{s}i\v{c}, Scapellato and Zagaglia Salvi in 1989 by constructing a family
of stable circulant graphs with compatible adjacency matrices
On the Normality of Cayley Digraphs of Groups of Order Twice a Prime
We call a Cayley digraph X = Cay(G, 8) normal for G if the right regular representation R ( G) of G is normal in the full automorphism group Aut(X) of X. In this paper we determine the normality of Cayley digraphs of groups of order twice a prime.