Deza graphs with parameters (v,k,k−2,a)

Abstract

A Deza graph with parameters is a ‐regular graph on vertices in which the number of common neighbors of two distinct vertices takes one of the following values: or , where . In the previous papers Deza graphs with were characterized. In this paper, we characterize Deza graphs with .

Divisible design graphs with parameters $(4n,n+2,n-2,2,4,n)$ and $(4n,3n-2,3n-6,2n-2,4,n)$

“…If n is even, then the quotient matrix R of G equals one of matrices ( 4), ( 5) or ( 6) (6), then G is isomorphic to one of the graphs obtained from Construction 5.…”

“…Let G be a DDG with parameters (4n, n + 2, n − 2, 2, 4, n) and the quotient matrix (6). Further, let A = [A i j ] be the adjacency matrix of G with blocks A i j corresponding to a canonical partition of G. Now consider an auxiliary graph G * with the following adjacency matrix…”

“…Then we can switch edges between V 1 and V 2 and also between V 3 and V 4 . This switching gives us the DDG with parameters (4n, n + 2, n − 2, 2, 4, n) and quotient matrix (6).…”

Quasi-strongly regular graphs of grade three with diameter two

“…In fact the authors were inspired by Deza and Deza [5] who provided relationship of some Deza graph in their work concerning metric polytope. For more example of studies in Deza graphs see [12,15,16]. Another generalization of strongly regular graphs is the concept of quasi-strongly regular graphs which was introduced in Golightly et.…”