A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs |
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| Authors: | Sandi Klavžar Khaled Salem |
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| Institution: | 1. Faculty of Mathematics and Physics, University of Ljubljana, Slovenia;2. Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia;3. Department of Basic Sciences, The British University in Egypt, El Shorouk, Egypt |
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| Abstract: | 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 is alternating and each inner vertex has degree two. This extends a result from X. Guo, F. Zhang, -cycle resonant graphs, Discrete Math. 135 (1994) 113–20] that a hexagonal system is 1-cycle resonant if and only if it is catacondensed. |
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