  in the mathematical field of graph theory, an edge-transitive graph is a graph g such that, given any two edges e1 and e2 of g, there is an automorphism of g that maps e1 to e2. in other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges. ==examples and properties==  edge-transitive graphs include any complete bipartite graph k_{m,n}, and any symmetric graph, such as the vertices and edges of the cube. symmetric graphs are also vertex-transitive (if they are connected), but in general edge-transitive graphs need not be vertex-transitive. the gray graph is an example of a graph which is edge-transitive but not vertex-transitive. all such graphs are bipartite, and hence can be colored with only two colors. an edge-transitive graph that is also regular, but not vertex-transitive, is called semi-symmetric. the gray graph again provides an example. every edge-transitive graph must be bipartite and either semi-symmetric or biregular.. == see also == * edge-transitive (in geometry) ==references==  == external links == * 
Algebraic_graph_theory Graph_families