Abstract A finite simple graph $$\Gamma $$ Γ is called a Nest if it regular of valency 6 and admits an automorphism with two orbits the same length such that at least one subgraphs induced by these cycle. In this paper, we complete classification edge-transitive graphs solve problem posed Jajcay et al. (Elect...

A characterization is given of a class of edge-transitive Cayley graphs, providing methods for constructing Cayley graphs with certain symmetry properties. Various new half-arc transitive graphs are constructed. © 2004 Elsevier Ltd. All rights reserved.

A finite simple graph Γ is called a Nest if it regular of valency 6 and admits an automorphism ρ with two orbits the same length such that at least one subgraphs induced by these cycle. We say core-free no non-trivial subgroup group generated normal in Aut(Γ). In this paper, we show that, edge-transitive core-free, then isomorphic to following graphs: complement Petersen graph, Hamming H(2,4), ...

This paper considers the concept of restricted edge-connectivity, and relates that to the edgedegree of a connected graph. The author gives some necessary conditions for a graph whose restricted edge-connectivity is smaller than its minimum edge-degree, then uses these conditions to show some large classes of graphs, such as all connected edge-transitive graphs except a star, and all connected ...