Table of Contents
International Journal of Combinatorics
Volume 2015, Article ID 152918, 12 pages
http://dx.doi.org/10.1155/2015/152918
Research Article

The Class of -Cliqued Graphs: Eigen-Bi-Balanced Characteristic, Designs, and an Entomological Experiment

1Mathematics, UKZN, King George V Avenue, Glenwood, Durban 4041, South Africa
2ARC-PPRI, Private Bag X6006, Hilton 3245, South Africa

Received 29 September 2014; Revised 16 January 2015; Accepted 17 January 2015

Academic Editor: Laszlo A. Szekely

Copyright © 2015 Paul August Winter et al. 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

Much research has involved the consideration of graphs which have subgraphs of a particular kind, such as cliques. Known classes of graphs which are eigen-bi-balanced, that is, they have a pair a, b of nonzero distinct eigenvalues, whose sum and product are integral, have been investigated. In this paper we will define a new class of graphs, called q-cliqued graphs, on vertices, which contain cliques each of order connected to a central vertex, and then prove that these -cliqued graphs are eigen-bi-balanced with respect to a conjugate pair whose sum is and product . These graphs can be regarded as design graphs, and we use a specific example in an entomological experiment.