Cubic graphs with 62 vertices having the same path layer matrix

The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all paths in G. The entry (i,j) in this matrix is the number of simple paths in G having initial vertex v and length j. It was known that there are cubic graphs on 90 vertices having the same path layer matrix (Dobrynin, 1990). A new upper bound for the least order of cubic graphs with the same path layer matrix is presented. © 1993 John Wiley & Sons, Inc.