Affiliation:
1. College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongwen Road, Nan'an District, Chongqing 400065, China
Abstract
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.
Funder
Science and Technology Research Program of Chongqing Municipal Educational Committee