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The Connectivity and Diameter of Second Order Circuit Graphs of Matroids

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Abstract

Let C 2(M) be the second order circuit graph of a simple connected matroid M, then C 2(M) is 2-connected if M has more than one circuit and M is not a line. Moreover, C 2(M) has diameter at most two if and only if M does not have any restriction isomorphic to U 2,6.

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Authors and Affiliations

  1. Department of Mathematics, Huizhou University, Huizhou, 561007, Guangdong, China

    Jinquan Xu

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26506, USA

    Ping Li & Hong-Jian Lai

  3. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 630046, Xinjiang, China

    Hong-Jian Lai

Authors
  1. Jinquan Xu
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  2. Ping Li
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  3. Hong-Jian Lai
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Correspondence to Ping Li.

Additional information

This work is supported by the National Natural Science Foundation of China (61070230).

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Xu, J., Li, P. & Lai, HJ. The Connectivity and Diameter of Second Order Circuit Graphs of Matroids. Graphs and Combinatorics 28, 737–742 (2012). https://doi.org/10.1007/s00373-011-1074-6

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  • DOI: https://doi.org/10.1007/s00373-011-1074-6

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