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Sufficient Condition and Algorithm for Hamiltonian in 3-Connected 3-Regular Planar Bipartite Graph
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 117 - Number 11 |
| Year of Publication: 2015 |
| Authors: Md. Khaliluzzaman, Md. Monirul Islam, Md. Monjur Hasan |
10.5120/20596-3096
|
Md. Khaliluzzaman, Md. Monirul Islam, Md. Monjur Hasan . Sufficient Condition and Algorithm for Hamiltonian in 3-Connected 3-Regular Planar Bipartite Graph. International Journal of Computer Applications. 117, 11 ( May 2015), 6-10. DOI=10.5120/20596-3096
Abstract
A graph G (V, E) is said to be Hamiltonian if it contains a spanning cycle. The spanning cycle is called a Hamiltonian cycle of G and G is said to be a Hamiltonian graph. A Hamiltonian path is a path that contains all the vertices in V (G) but does not return to the vertex in which it began. In this paper, we study Hamiltonicity of 3-connected, 3-regular planar bipartite graph G with partite sets V=M ? N. We shall prove that G has a Hamiltonian cycle if G is balanced with M = N. For that we present an algorithm for a bipartite graph KM,N where M>3, N>3 and M,N both are even to possess a Hamiltonian cycle. In particular, we also prove a theorem for S proper subset (M or N) of V the number of components W (G-S) = S implies the graph has a Hamiltonian path.
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