Strictly Deza line graphs

• Published in: Proceedings of the Steklov Institute of Mathematics Vol. 285; no. Suppl 1; pp. 78 - 90
• Main Authors: Kabanov, V. V., Mityanina, A. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-06-2014
• Subjects: Mathematics; Mathematics and Statistics; line graphs; strictly Deza graphs
• ISSN: 0081-5438; 1531-8605
• DOI: 10.1134/S0081543814050083

For a given graph
G
, its line graph
L
(
G
) is defined as the graph with vertex set equal to the edge set of
G
in which two vertices are adjacent if and only if the corresponding edges of
G
have exactly one common vertex. A
k
-regular graph of diameter 2 on
υ
vertices is called a strictly Deza graph with parameters (
υ, k, b, a
) if it is not strongly regular and any two vertices have
a
or
b
common neighbors. We give a classification of strictly Deza line graphs.