On Connected m-HPK(n1,n2,n3,n4)[Kt]-Residual Graphs

We define m-HPK(n1,n2,n3,n4)[Kt]-residual graphs in which HPK is a hyperplane complete graph. We extend P. Erdös, F. Harary, and M. Klawe's definition of plane complete residual graph to hyperplane and obtain the hyperplane complete residual graph. Further, we obtain the minimum order of HPK(n1,n2,n3,n4)[Kt]-residual graphs and m-HPK(n1,n2,n3,n4)[Kt]-residual graphs. In addition, we obtain a unique minimal HPK(n1,n2,n3,n4)[Kt]-residual graphs and a unique minimal m-HPK(n1,n2,n3,n4)[Kt]-residual graphs