P 9 - Factorization of Complete Bipartite Graph
نویسنده
چکیده
Pk -factorization of a complete bipartite graph for k, an even integer was studied by H. Wang [1]. Further, Beiling Du [2] extended the work of H.Wang, and studied the P2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers[3,4,5]. P3-factorization of complete bipartite graph was studied by K.Ushio [3]. P5-factorization of complete bipartite graph was studied by J.Wang etal [4]. Further, P7-factorization was studied by J.Wang [5] and he gave necessary and sufficient conditions for its existence. In the present paper we study the P9-factorization of complete bipartite graph Km,n and show that the necessary and sufficient conditions for its existence are: (1) 5m ≥ 4n, (2) 5n ≥ 4m, (3) m + n ≡ 0(mod 9) and (4) 9mn/8(m + n) is an integer. Mathematics Subject Classification: 68R10, 05C70
منابع مشابه
Bipartite Symmetric Digraph
P2p -factorization of a complete bipartite graph for p, an integer was studied by Wang [1]. Further, Beiling [2] extended the work of Wang[1], and studied the P2k -factorization of complete bipartite multigraphs. For even value of k in Pk -factorization the spectrum problem is completely solved [1, 2, 3]. However for odd value of k i.e. P3 , P5 and P7 , the path factorization have been studied ...
متن کاملP3-factorization of complete bipartite symmetric digraphs
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 ...
متن کاملMixed cycle-E-super magic decomposition of complete bipartite graphs
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) + ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...
متن کاملMixed cycle-E-super magic decomposition of complete bipartite graphs
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...
متن کاملA Quantitative Approach to Perfect One-Factorizations of Complete Bipartite Graphs
Given a one-factorization F of the complete bipartite graph Kn,n, let pf(F) denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in F . Let pf(n) be the maximum of pf(F) over all one-factorizations F of Kn,n. In this work we prove that pf(n) > n2/4, for all n > 2. 1 Perfect one-factorizations A one-factorization of a graph G is a partition of its set o...
متن کامل