Mutually Independent Hamiltonian Cycles on Some Graphs in Interconnection Networks

• Main Authors: Hsun Su, 蘇珣
• Other Authors: Shin-Shin Kao
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/39053741506465950972

博士 === 中原大學 === 應用數學研究所 === 100 === Abstract Mutually independent hamiltonian cycles, abbreviated as MIHCs, have been studied on interconnection networks widely. In this dissertation, we study MIHCs on some specific graphs. We established the existence of MIHCs in $k$-ary $n$-cubes $(Q_{n}^{k})$ when $k$ is even, cycle composition networks $(CCN_k)$, alternating group graphs $(AG_n)$ and arrangement graphs $(A_{n,k})$. The results are shown to be optimal in the sense that the number of MIHCs we constructed is maximal. In addition to the construction schemes of MIHCs for specific graphs, we intend to give some sufficient and necessary conditions for the existence of MIHCs in general graphs. A conjecture is given based on known results.