| Abstract: | The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all possible paths in G. The entry (i,j) of this matrix is the number of paths in G having initial vertex i and length j. It is known that there are cubic graphs on 62 vertices having the same path layer matrix (A. A. Dobrynin. J Graph Theory 17 (1993) 1–4). A new upper bound of 36 vertices for the least order of such cubic graphs is established. This bound is realized by cubic graphs without cut‐vertices. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 177–182, 2001 |
