On Quasi-strongly Regular Graphs with Parameters (n,k,a;k-2,c2) (I)

A graph is called an edge-regular graph with parameters (n, k, a) if it is a k-regular graph with n vertices and any two adjacent vertices have a common neighbours. A quasi-strongly regular graph with parameters (n , k , a ; c 1 , c 2) , denoted by QSRG (n , k , a ; c 1 , c 2) , is an edge-regular graph with parameters (n, k, a) in which any two non-adjacent vertices have c 1 or c 2 common neighbours. A quasi-strongly regular graph is called a strictly quasi-strongly regular graph if it is neither a strongly regular graph nor a Deza graph. The purpose of our research is to complete the structural characterization of strictly QSRG (n , k , a ; k - 2 , c 2) . In an earlier paper, we characterised QSRG (n , k , a ; k - 2 , c 2) satisfying a < k - 5 and l 1 > 2 , where l 1 is the number of vertices with k - 2 common neighbours with a given vertex. In the present paper, we investigate the structural characterization of strictly QSRG (n , k , a ; k - 2 , c 2) satisfying a ≥ k - 5 . [ABSTRACT FROM AUTHOR]