International Journal of Computer Applications |
Foundation of Computer Science (FCS), NY, USA |
Volume 73 - Number 18 |
Year of Publication: 2013 |
Authors: U. S. Rajput, Bal Govind Shukla |
10.5120/12845-0234 |
U. S. Rajput, Bal Govind Shukla . (P_5)- Factorization of Complete Bipartite Symmetric Digraphs. International Journal of Computer Applications. 73, 18 ( July 2013), 40-45. DOI=10.5120/12845-0234
In path factorization, H. Wang [1] gives the necessary and sufficient conditions for the existence of P_k-factorization of a complete bipartite graph for k, an even integer. Further, Beiling Du [2] extended the work of H. Wang, and studied the P_2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers. P_3-factorization of complete bipartite graph was studied by K. Ushio [3]. P_5-factorization of complete bipartite graph was studied by J. Wang [4]. In the present paper, we study (P_5 ) ?-factorization of complete bipartite symmetric digraphs and show that the necessary and sufficient conditions for the existence of (P_5 ) ?-factorization of complete bipartite symmetric digraphs are: (1)3m?2n, (2) 3n?2m, (3)m+n?0(mod 5) and (4)5mn/2(m+n) is an integer. Mathematics Subject Classification 68R10, 05C70, 05C38.