Abstract
Let G be a simple 3-connected graph. An edge e of G is essential if neither the deletion G\ e nor the contraction G/e is both simple and 3-connected. In this study, we show that all 3-connected graphs with k(k ≥ 2) non-essential edges can be obtained from a wheel by three kinds of operations which defined in the paper.
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Liu, Y. The 3-Connected Graphs with Exactly k Non-Essential Edges. Graphs and Combinatorics 26, 119–131 (2010). https://doi.org/10.1007/s00373-010-0873-5
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DOI: https://doi.org/10.1007/s00373-010-0873-5