Tetravalent vertex- and edge-transitive graphs over doubled cycles

The vertex-transitive and edge-transitive tetravalent graphs of square-free order

In this paper, a classification is given for tetravalent graphs of square-free order which are vertex-transitive and edge-transitive. It is shown that such graphs are Cayley graphs, edge-regular metacirculants and covers of some graphs arisen from simple groups A7, J1 and PSL(2, p).

Tetravalent half-edge-transitive graphs and non-normal Cayley graphs

Hamilton cycles in dense vertex-transitive graphs

Tetravalent Graphs Admitting Half-Transitive Group Actions: Alternating Cycles

In this paper we study finite, connected, 4-valent graphs X which admit an action of a group G which is transitive on vertices and edges, but not transitive on the arcs of X. Such a graph X is said to be (G, 1 2)-transitive. The group G induces an orientation of the edges of X, and a certain class of cycles of X (called alternating cycles) determined by the group G is identified as having an im...

Vertex Removable Cycles of Graphs and Digraphs

‎In this paper we defined the vertex removable cycle in respect of the following‎, ‎if $F$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$G in F $‎, ‎the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $.‎ ‎The vertex removable cycles of eulerian graphs are studied‎. ‎We also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎