The Electronic Journal of Combinatorics

v15i1n3 — Comment by the editors, Feb 11, 2008.

In the note [N3] in Volume 15 (1) entitled "Extension of Strongly Regular Graphs" by Raluca Gera and Jian Shen, a generalization of strongly regular graphs is defined which relaxes the regularity property of vertex degrees. A characterization is given which is a generalization of the well-known "Friendship theorem." We are grateful to Mikhail Klin and Alexander Kelmans for bringing to our attention the following fact concerning this generalization.

Kelmans defined the same generalization of strongly regular graphs and obtained the same characterization in the paper:

[K] A.K. Kelmans, Graphs with the same numbers of paths of length two between adjacent and between two non-adjacent vertices (in Russian). In Voprosy Kibernetiki, Moscow (1973) 70-75.

The proofs in [K] and [N3] are different but both depend on counting arguments.