Journal of Jianghan University (Natural Science Edition) ›› 2020, Vol. 48 ›› Issue (5): 36-41.doi: 10.16389/j.cnki.cn42-1737/n.2020.05.004

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Hamilton Properties of Second-Order Cyclic Graphs of Uniform Matroid

LIU Bina，DENG Zijiana，DU Qingsonga，HUO Bofeng*a，b，LI Faxuc，d   

  1. a. School of Mathematics and Statistic，b. Key Laboratory of the Internet of Things of Qinghai Province，c. School of Computer Science，d. Laboratory of Tibetan Information Processing，Qinghai Normal University，Xining 810008，Qinghai，China
  • Published:2020-09-22
  • Contact: 火博丰
  • Supported by:
    青海省自然科学基金资助项目（11961055）；青海省自然基金资助项目（2018-ZJ-718）

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Abstract: Hamilton properties of second-order cyclic graphs of uniform matroid under certain conditions were studied. From Hamilton properties of second-order cyclic graphs of U2,n and U3,n under certain conditions，generalizing to Hamilton properties of second-order cyclic graphs of Um,n under certain conditions. We discovered second-order cyclic graphs of Um,n was Hamiltonian-connected and uniformly Hamilton，if n = m + 2,m + 3,?,2m，m，n were positive integer and m ≥ 2,n ≥ m + 2.

Key words: uniform matroid, cyclic graph of matroids, Hamiltonian-connected, uniformly Hamilton

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