COMPUTING THE ANTI-KEKULÉ NUMBER OF CERTAIN NANOTUBES AND NANOCONES

Authors

  • Mehar Ali MALIK Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan. Email: alies.camp@gmail.com. https://orcid.org/0000-0002-5666-3968
  • Muhammad IMRAN Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan. Email: drmimranchaudhry@gcuf.edu.pk. https://orcid.org/0000-0002-6591-0991

Keywords:

Perfect matching, Anti-Kekulé number, Nanotubes, Nanocones

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 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.

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STUDIA UBB CHEMIA, Volume 60 (LX), No. 2, June 2015

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Published

2015-06-30

How to Cite

MALIK, M. A. ., & IMRAN, M. . (2015). COMPUTING THE ANTI-KEKULÉ NUMBER OF CERTAIN NANOTUBES AND NANOCONES. Studia Universitatis Babeș-Bolyai Chemia, 60(2), 229–240. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/chemia/article/view/8445

Issue

Volume 60, No. 2, Tom II, 2015

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Articles

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Copyright (c) 2015 Studia Universitatis Babeș-Bolyai Chemia

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