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.[1]
In other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges.
Contents |
Examples and properties
Edge-transitive graphs include any complete bipartite graph Km,n, and any symmetric graph, such as the vertices and edges of the cube.[1] 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,[1] 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.
See also
- Edge-transitive (in geometry)
References
- ^ a b c Biggs, Norman (1993). Algebraic Graph Theory (2nd ed. ed.). Cambridge: Cambridge University Press. p. 118. ISBN 0-521-45897-8.
External links
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
