On the anti-Kekule number of cubic graphs

Minisymposium: CHEMICAL GRAPH THEORY

Content: The anti-Kekul\'{e} number of a connected graph $G$ is the smallest number of edges to be removed to create a connected subgraph without perfect matchings. In this article, we show that the anti-Kekul\'{e} number of a 2-connected cubic graph is either 3 or 4, and the anti-Kekul\'{e} number of a connected cubic bipartite graph is always equal to 4. Moreover, direct application of these results show that the anti-Kekul\'{e} number of a boron-nitrogen fullerene is 4 and the anti-Kekul\'{e} number of a (3,6)-fullerene is 3.

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