## Abstract

Let G(V,E) be a connected graph. A set M subset of E is called a matching if no two edges in M have a common end-vertex. A matching M in G is perfect if every vertex of G is incident with an edge in M. The perfect matchings correspond to Kekulé structures which play an important role in the analysis of resonance energy and stability of hydrocarbons. The anti-Kekulé number of a graph G, denoted as ak(G), is the smallest number of edges which must be removed from a connected graph G with a perfect matching, such that the remaining graph stay connected and contains no perfect matching. In this paper, we calculate the anti-Kekulé number of TUC_{4}C_{8}(S)[p,q] nanotube, TUC_{4}C_{8}(S)[p,q] nanotori for all positive integers p, q and CNC_{2k-1}[n] nanocones for all positive integers k and n.

Original language | English |
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Pages (from-to) | 229-240 |

Number of pages | 12 |

Journal | Studia Universitatis Babes-Bolyai Chemia |

Volume | 60 |

Issue number | 2 |

Publication status | Published - Jun 1 2015 |

Externally published | Yes |

## Keywords

- Anti-Kekulé number
- Nanocones
- Nanotubes
- Perfect matching

## ASJC Scopus subject areas

- General Chemistry