Infinite series of Deza graphs with strongly regular children · arXivDeskAbstract
A graph Γ is called a Deza graph with parameters (n,k,b,a) if it has exactly n vertices, is k-regular, and for any two distinct vertices u
and
, the number of common neighbors of
and
is either
or
. The graphs
and
, which have the same vertex set as
, and in which two vertices are adjacent if they have
or
common neighbours, respectively, are called the children of the Deza graph. If, for a Deza graph
, both
and
are strongly regular graphs, then
is called a strongly Deza graph. In this work, we present a construction of an infinite family of strongly Deza graphs, for which the children
and
are strongly regular graphs with the same parameters as the graphs
NOnε⊥(5) and
NOnε⊥(5) .