Computing the anti-Kekulé number of certain nanotubes and nanocones

Mehar Ali Malik, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 TUC4C8(S)[p,q] nanotube, TUC4C8(S)[p,q] nanotori for all positive integers p, q and CNC2k-1[n] nanocones for all positive integers k and n.

Original languageEnglish
Pages (from-to)229-240
Number of pages12
JournalStudia Universitatis Babes-Bolyai Chemia
Issue number2
Publication statusPublished - Jun 1 2015
Externally publishedYes


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

ASJC Scopus subject areas

  • General Chemistry


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