Abstract Quasi-strongly regular graphs are a combinatorial generalization of strongly regular graphs. A quasi-strongly regular graph of grade 2 with parameters ( n , k , a ; c 1 , c 2 ) is a k -regular graph on n vertices such that any two adjacent vertices have a common neighbours, any two non-adjacent vertices have c 1 or c 2 common neighbours, and for each c i ( i = 1 , 2 ) , there exists a pair of non-adjacent vertices sharing c i common neighbours. If a quasi-strongly regular graph of grade 2 is neither a strongly regular graph nor a Deza graph, then it is called a strictly quasi-strongly regular graph. In this paper, we characterize strictly quasi-strongly regular graphs with parameters satisfying c 1 = k − 1 .

中文翻译：

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在具有参数 (n,k,a;k−1,c2) 的准强正则图上

摘要 拟强正则图是强正则图的组合推广。具有参数 ( n , k , a ; c 1 , c 2 ) 的 2 级准强正则图是 n 个顶点上的 ak -正则图，使得任何两个相邻顶点都有一个公共邻居，任何两个不相邻顶点都有c 1 或c 2 公共邻居，对于每个ci ( i = 1 , 2 ) ，存在一对非相邻顶点共享ci 公共邻居。如果 2 级的拟强正则图既不是强正则图也不是 Deza 图，则称其为严格拟强正则图。在本文中，我们刻画了参数满足 c 1 = k − 1 的严格准强正则图。