The Cyclic Edge Connectivity and Anti-Kekulé Number of the (5,6,7)-Fullerene

Abstract

ABSTRACTA plane cubic graph is called a (5,6,7)-fullerene if its faces are only composed of pentagons, hexagons and heptagons. In this paper, we completely characterize the cyclic edge-connectivity of the (5,6,7)-fullerene. Furthermore, we obtain that the anti-Kekulé number of the (5,6,7)-fullerene is 4 when the cyclic edge-connectivity is larger then three. In particular, we obtain some properties with respect to the anti-Kekulé number of the (5,6,7)-fullerene with cyclic 3 edge-connectivity if it is 2-extendable.