Super Connectivity of A Family of Direct Product Graphs

Let g1 and g2 be two graphs. the kronecker product g1 × g2 has vertex set v (g1 × g2) =v (g1) × v (g2) and the edge set e(g1 × g2) = f(u1; v1); (u2; v2) j u1u2 2 e(g1); v1v2 2 e(g2)g: in thistalk we show that if kp1;p2;··· ;pr is a complete multipartite graph, where the parameters p1; p2; · · · ; prsatisfying certain conditions and pn is a path of length n − 1, then kp1;p2;··· ;pr × pn is not super-k(i),where 1 ≤ i ≤ n − 1 and n ≥ 2. also we show that kp1;p2;··· ;pr × cn is not super-k0, where cn is a cycleof length n and n ≥ 3.