@inproceedings{62e012f6411d4129861ec6f349db0c9c,
title = "Necessary and sufficient conditions for hamiltonian based on linear diophantine equation systems with cycle vector",
abstract = "Two necessary and sufficient conditions are presented for Hamiltonian cycle problem in simple undirected graph using linear Diophantine equation systems with cycle vector. The first one is based on the incidence matrix and the second one is based on edge-adjacency matrix. It is proven that the solution set of the cycle vector correspond to the edges of Hamiltonian cycle in a given graph. Based on these result conditions, two necessary conditions for the Hamiltonian graph are given by determining the rank of the matrix.",
keywords = "Cycle vector, Edge adjacency matrix, Hamiltonian cycle, Incidence matrix, Linear diophantine equation system, Rank",
author = "Guohun Zhu and Chunwei Song and Kaoru Hirota and Fangyan Dong and Yonghua Wu",
year = "2009",
doi = "10.1109/WGEC.2009.215",
language = "English",
isbn = "9780769538990",
series = "3rd International Conference on Genetic and Evolutionary Computing, WGEC 2009",
pages = "847--850",
booktitle = "3rd International Conference on Genetic and Evolutionary Computing, WGEC 2009",
note = "3rd International Conference on Genetic and Evolutionary Computing, WGEC 2009 ; Conference date: 14-10-2009 Through 17-10-2009",
}