Hamiltonian properties of Cartesian product graphs

• Main Authors: Kao, Louis, 高至芃
• Other Authors: Weng, Chih-Wen
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/11145140587390054943

碩士 === 國立交通大學 === 應用數學系所 === 104 === The Cartesian product of two graphs forms a special class of graphs. First,for a given tree through its Cartesian products withcycles, we discuss its Hamiltonicity and edge-Hamiltonicity. Second, for a given tree through its Cartesian products with paths, we discuss its Hamiltonicity and even-pancyclicity. We find several Hamiltonian graphs in the case that the tree has a perfect matching or a path factor. Some well-known results which have been proved are also given in this thesis with modified results or new approach of proofs. In particular, we prove that the two conditions Hamiltonian and 1-tough are equivalent in those graphs we discussed.