Table of Contents
Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 983830, 7 pages
http://dx.doi.org/10.1155/2013/983830
Research Article

On Connected m-HPK-Residual Graphs

College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongwen Road, Nan'an District, Chongqing 400065, China

Received 27 November 2012; Revised 20 January 2013; Accepted 22 January 2013

Academic Editor: Pantelimon Stǎnicǎ

Copyright © 2013 Huiming Duan and Yonghong Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define m-HPK-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-residual graphs and m-HPK-residual graphs. In addition, we obtain a unique minimal HPK-residual graphs and a unique minimal m-HPK-residual graphs.