On the anti-kekulé number of nanotubes and nanocones

Mehar Ali Malik, Sakander Hayat, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Let G(V,E)be a connected graph. A set M ⊆ 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 akG, 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. The anti-Kekulé numbers of silicate, oxide and honeycomb networks were calculated in [Xavier, Shanthi, and Raja, International Journal of Pure and Applied Mathematics 6, 1019 (2013)]. In this paper, we calculate the anti-Kekulé number of HAC5C7/2p(q), TUC4(C8)R,2p(q), ∀ pq nanotubes and CNC2kn, ∀ k(n) nanocones. We set the infinite cases of all nanotubes as conjecture.

Original languageEnglish
Pages (from-to)3125-3129
Number of pages5
JournalJournal of Computational and Theoretical Nanoscience
Issue number10
Publication statusPublished - Oct 2015
Externally publishedYes


  • Anti-Kekulé Number
  • Matching
  • Nanocones
  • Nanotubes
  • Perfect Matching

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science
  • Condensed Matter Physics
  • Computational Mathematics
  • Electrical and Electronic Engineering


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