Symmetric Graph

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical field of graph theory, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of linked vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called 1-arc-transitive or flag-transitive. By definition (ignoring u1 and u2), a symmetric graph without isolated vertices must also be vertex transitive. Since the definition above maps one edge to another, a symmetric graph must also be edge transitive. However, an edge-transitive graph need not be symmetric, since a-b might map to c-d, but not to d-c. Semi-symmetric graphs, for example, are edge-transitive and regular, but not vertex-transitive.

Pagina's: 84, Paperback, Betascript Publishers