A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs

作者：Klavzar Sandi; Salem Khaled^*

来源：Discrete Applied Mathematics, 2012, 160(7-8): 1277-1280.

DOI：10.1016/j.dam.2011.12.030

• Bipartite plane graph
• 1-cycle resonant graph
• Hexagonal system
• Alternating cycle

It is proved that a bipartite 2-connected plane graph in which the common boundary of adjacent faces is a simple curve is 1-cycle resonant if and only if the outer face of G is alternating and each inner vertex has degree two. This extends a result from [X. Guo, F. Zhang, k-cycle resonant graphs, Discrete Math. 135 (1994) 113-20] that a hexagonal system is 1-cycle resonant if and only lilt is catacondensed.

• 出版日期2012-5