On Connected m-HPK(n1, n2, n3, n4)[Kt]-Residual Graphs. (12th March 2013)

• Record Type: Journal Article
• Authors: Duan, Huiming; Li, Yonghong
• Other Names: Stǎnicǎ Pantelimon Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2013(2013)
• Publication Date: 2013-03-12
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2013/983830
• Languages: English
• ISSNs: 2090-9837

Abstract

Abstract : We define m - HPK ( n 1, n 2, n 3, n 4 ) [ K t ] -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 ( n 1, n 2, n 3, n 4 ) [ K t ] -residual graphs and m - HPK ( n 1, n 2, n 3, n 4 ) [ K t ] -residual graphs. In addition, we obtain a unique minimal HPK ( n 1, n 2, n 3, n 4 ) [ K t ] -residual graphs and a unique minimal m - HPK ( n 1, n 2, n 3, n 4 ) [ K t ] -residual graphs.