Journal of East China Normal University(Natural Sc

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Probing equivalent definitions of 2-edge connected graphs

SU Jing, MA Fei, YAO Bing   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2015-12-29 Online:2017-01-25 Published:2017-01-13


As known, k-edge connected graphs play an important role in the research of networks and graph theory. There are many propositions of 2-edge connected graphs nowadays, which depict the essences of 2-edge connected graphs. We present 17 equivalent propositions of 2-edge connected graphs and dig more properties of 2-edge connected graphs from different aspects of 2-edge connected graphs. Furthermore, two equivalent propositions of 2-edge connected graphs by two new operations are proposed, and then we provide the equivalent proofs between the propositions we have collected and discovered.

Key words: 2-edge connected graph, ear edge decomposition, block, trail, cycle