Comment on Volume 15(1), article N3
(Feb 11, 2008)
Extension of Strongly Regular Graphs
Raluca Gera and Jian Shen
Comment
by the editors, March 12, 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.