CLASSIFICATION OF TRIVALENT SYMMETRIC GRAPHS OF SMALL ORDER Marston Conder and Margaret Morton Department of Mathematics University of Auckland Private Bag 92019 Auckland NEW ZEALAND A classification is given of all finite connected trivalent symmetric graphs on up to 240 vertices, based on an analysis of short relators in their automorphism groups. SUBJECT CLASSIFICATION 05C25(Primary) 20F05(S...

The growth function of a graph with respect to a vertex is near polynomial if there exists a polynomial bounding it above for infinitely many positive integers. In the paper vertex-symmetric undirected graphs and vertex-symmetric directed graphs with coinciding inand out-degrees are described in the case their growth functions are near polynomial.

The symmetric m-th power of a graph is the graph whose vertices are m-subsets of vertices and in which two m-subsets are adjacent if and only if their symmetric difference is an edge of the original graph. It was conjectured that there exists a fixed m such that any two graphs are isomorphic if and only if their m-th symmetric powers are cospectral. In this paper we show that given a positive i...