A ClaSSification of Solvable Symmetric Graphs of Order 6p

Abstract:

      Let X be a simple undirected graph and G a subgroup of Aut(X).X is said to beG-symmetric if G acts transitively on the set of ordered adjacent pairs of vertices of X.X is said to be symmetric if it is Aut(X)-symmetric. X is said to be solvable symmetricgraph if Aut(x)contains a solvable subgroup G such that X is G-symmetric,In thispaper we give a classification for solvable symmetric graphs of order 6p where p≥5 is aprlme.