Packings and Coverings of Various Complete Graphs with the 4-Cycle with a Pendant EdgeReport as inadecuate




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ISRN CombinatoricsVolume 2013 2013, Article ID 236298, 8 pages

Research Article

Department of Computer Science, Francis Marion University, Florence, SC 29502, USA

Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK

Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USA

Received 17 June 2013; Accepted 12 August 2013

Academic Editors: C. da Fonseca, P. E. Jorgensen, A. V. Kelarev, and S. Zhou

Copyright © 2013 Brandon Coker 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

We consider the packings and coverings of complete graphs with isomorphic copies of the 4-cycle with a pendant edge. Necessary and sufficient conditions are given for such structures for 1 complete graphs , 2 complete bipartite graphs , and 3 complete graphs with a hole . In the last two cases, we address both restricted and unrestricted coverings.





Author: Brandon Coker, Gary D. Coker, Robert Gardner, and Yan Xia

Source: https://www.hindawi.com/



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