Department of Mathematics
Maximal resonance of cubic bipartite polyhedral graphs
Let H be a set of disjoint faces of a cubic bipartite polyhedral graph G. If G has a perfect matching M such that the boundary of each face of H is an M-alternating cycle (or in other words, G - H has a perfect matching), then H is called a resonant pattern of G. Furthermore, G is k-resonant if every i (1 ≤ i ≤ k) disjoint faces of G form a resonant pattern. In particular, G is called maximally resonant if G is k-resonant for all integers k ≥ 1. In this paper, all the cubic bipartite polyhedral graphs, which are maximally resonant, are characterized. As a corollary, it is shown that if a cubic bipartite polyhedral graph is 3-resonant then it must be maximally resonant. However, 2-resonant ones need not to be maximally resonant. © 2010 Springer Science+Business Media, LLC.
Cyclical edge-connectivity, k-resonant, Polyhedral graph
Source Publication Title
Journal of Mathematical Chemistry
Link to Publisher's Edition
Shiu, Wai Chee, Heping Zhang, and Saihua Liu. "Maximal resonance of cubic bipartite polyhedral graphs." Journal of Mathematical Chemistry 48.3 (2010): 676-686.