Small regular graphs having the same path layer matrix*

The path layer matrix of 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 i and length j. Some new upper bounds for r‐regular graphs with the same path layer matrix are presented for r=4, 5, 6. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 219–221, 2002; DOI 10.1002/jgt.10005