{"title":"N-Sun Decomposition of Complete, Complete Bipartite and Some Harary Graphs","authors":"R. Anitha, R. S. Lekshmi","volume":19,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":452,"pagesEnd":458,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/3193","abstract":"Graph decompositions are vital in the study of\ncombinatorial design theory. A decomposition of a graph G is a\npartition of its edge set. An n-sun graph is a cycle Cn with an edge\nterminating in a vertex of degree one attached to each vertex. In this\npaper, we define n-sun decomposition of some even order graphs\nwith a perfect matching. We have proved that the complete graph\nK2n, complete bipartite graph K2n, 2n and the Harary graph H4, 2n have\nn-sun decompositions. A labeling scheme is used to construct the n-suns.","references":"[1] W. D. Wallis, \"Magic graphs,\" Birkhauser, 2000.\n[2] B. Alspach, J. C. Bermond and Sotteau, \"Decompositions into cycles I:\nHamilton decompositions, cycles and rays,\" Kluwer Academic Press\n1990, pp. 9-18.\n[3] B. Alspach, \"The wonderful Walecki construction,\" 2006, April [Lecture\nnotes].\n[4] B. Alspach and H. Gavlas, \"Cycle decompositioins of Kn and Kn - I,\" J.\nCombin.. Theory Ser. B, Vol. 81, pp. 77-99, 2001.\n[5] D. B. West, \"Introduction to graph theory,\" Pearson Education Pte.Ltd.,\n2002.\n[6] J. L. Gross and J. Yellen, \"Handbook of Graph theory,\" CRC Press,\n2004.\n[7] R. Laskar and B. Auerbach, \"On decomposition of r-partite graphs into\nedge-disjoint Hamilton circuits\", Discrete Math. Vol. 14, pp. 265-268,\n1976.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 19, 2008"}