A　cornerstone　contribution　due　to　Chung,　Graham　and　Wilson　(1989)　implies　that　many　graph　properties　of　different　na-ture　are　equivalent.　Graphs　that　satisfy　any　(and　thus　all)　of　the　properties　are　called　quasi-random　graphs.　In　this　paper,　we　con-struct　families　of　quasi-random　graphs　for　any　given　edge　density,　which　are　regular　but　not　strongly　regular.　Moreover,　we　obtain　a　lower　bound　for　Ramsey　number　r(K1　+　G)　in　which　the　graph　G　contains　no　isolated　vertex,　which　extends　a　classical　result　by　Shearer　and　Mathon