TY - JOUR
T1 - Maximal resonance of cubic bipartite polyhedral graphs
AU - Shiu, Wai Chee
AU - Zhang, Heping
AU - Liu, Saihua
N1 - Funding Information:
This work is supported by NSFC (grant no. 10831001) and FRG, Hong Kong Baptist University.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - Cyclical edge-connectivity
KW - k-resonant
KW - Polyhedral graph
UR - http://www.scopus.com/inward/record.url?scp=77956441735&partnerID=8YFLogxK
U2 - 10.1007/s10910-010-9700-8
DO - 10.1007/s10910-010-9700-8
M3 - Journal article
AN - SCOPUS:77956441735
SN - 0259-9791
VL - 48
SP - 676
EP - 686
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 3
ER -