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), ...

Slovenija Abstract An innnite family of cubic edge-transitive but not vertex-transitive graph graphs with edge stabilizer isomorphic to Z Z 2 is constructed.

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.

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 ...

This paper introduces a family of tetravalent graphs called rose window graphs, denoted by Rn(a, r), and investigates their symmetry properties. Four families of these graphs are shown to be edge-transitive and it is conjectured that every Rn(a, r) which is edge-transitive belongs to one of these families. Proofs and conjectures about the size of a dart-stabilizer and about regular maps contain...

A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...