Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 892839, 9 pages
Induced Graphoidal Decompositions in Product Graphs
1Department of Mathematics, Christ University, Bangalore, Karnataka 560029, India
2Department of Mathematics, The Madura College, Madurai, Tamil Nadu 625011, India
Received 25 July 2012; Revised 20 October 2012; Accepted 5 November 2012
Academic Editor: Annalisa De Bonis
Copyright © 2013 Mayamma Joseph and I. Sahul Hamid. 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.
- G. Chartrand and L. Lesniak, Graphs and Digraphs, CRC Press, Boca Raton, Fla, USA, 4th edition, 2005.
- F. Harary, “Covering and packing in graphs. I,” Annals of the New York Academy of Sciences, vol. 175, pp. 198–205, 1970.
- F. Harary and A. J. Schwenk, “Evolution of the path number of a graph: covering and packing in graphs. II,” in Graph Theory and Computing, R. C. Rad, Ed., pp. 39–45, Academic Press, New York, NY, USA, 1972.
- B. Péroche, “The path-numbers of some multipartite graphs,” Annals of Discrete Mathematics, vol. 9, pp. 195–197, 1980.
- R. G. Stanton, D. D. Cowan, and L. O. James, “Some results on path numbers,” in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory, and Computing, pp. 112–135, 1970.
- B. D. Acharya and E. Sampathkumar, “Graphoidal covers and graphoidal covering number of a graph,” Indian Journal of Pure and Applied Mathematics, vol. 18, no. 10, pp. 882–890, 1987.
- S. Arumugam, “Path covers in graphs,” in Lecture Notes of the National Workshop on Decompositions of Graphs and Product Graphs Held at Annamalai University, Tamil Nadu, India, January 2006.
- K. Ratan Singh and P. K. Das, “Induced graphoidal covers in a graph,” International Journal of Mathematical and Statistical Sciences, vol. 2, no. 3, pp. 102–106, 2010.
- K. Ratan Singh and P. K. Das, “Induced acyclic graphoidal covers in a graph,” International Journal of Computational and Mathematical Sciences, vol. 4, no. 7, pp. 333–339, 2010.
- I. Sahul Hamid and M. Joseph, “Further results on induced graphoidal decomposition,” submitted to. Discrete Mathematics, Algorithms and Applications.
- I. Sahul Hamid and M. Joseph, “Decomposition of graphs into internally disjoint induced paths,” submitted.
- R. Hammack, W. Imrich, and S. Klavžar, Handbook of Product Graphs, CRC Press, New York, NY, USA, 2nd edition, 2011.