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
Shiu, Wai Chee, Heping Zhang, and Saihua Liu. "Maximal resonance of cubic bipartite polyhedral graphs." Journal of Mathematical Chemistry 48.3 (2010): 676-686.