Labelings of type (1, 1, 1) for Klein bottle fullerenes

详细信息    查看全文

• 作者：Saad Ihsan Butt ; Muhammad Numan ; Shahid Qaisar
• 关键词：Klein bottle fullerene ; Klein bottle polyhex ; Super d ; antimagic labeling
• 刊名：Journal of Mathematical Chemistry
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：54
• 期：2
• 页码：428-441
• 全文大小：658 KB
• 参考文献：1.M. Bača, M. Miller, On \(d\) -antimagic labelings of type \((1,1,1)\) for prisms. J. Comb. Math. Comb. Comput. 44, 199–207 (2003)
  2.M. Bača, S. Jendrol’, M. Miller, J. Ryan, Antimagic labelings of generalized Petersen graphs that are plane. Ars Comb. 73, 115–128 (2004)
  3.M. Bača, E.T. Baskoro, S. Jendrol’, M. Miller, Antimagic labelings of hexagonal planar maps. Util. Math. 66, 231–238 (2004)
  4.M. Bača, Y. Lin, M. Miller, Antimagic labelings of grids. Util. Math. 72, 65–75 (2007)
  5.K.W. Lih, On magic and consecutive labelings of plane graphs. Util. Math. 24, 165–197 (1983)
  6.M. Bača, On magic labelings of grid graphs. Ars Comb. 33, 295–299 (1992)
  7.M. Bača, On magic labelings of honeycomb. Discrete Math. 105, 305–311 (1992)CrossRef
  8.M. Bača, F. Bashir, A. Semaničová, Face antimagic labelings of antiprisms. Util. Math. 84, 209–224 (2011)
  9.G. Ali, M. Bača, F. Bashir, A. Semaničová-Feňovčíková, On face antimagic labelings of disjoint union of prisms. Util. Math. 85, 97–112 (2011)
  10.M. Bača, L. Brankovic, A. Semaničová-Feňovčíková, Labelings of plane graphs containing Hamilton path. Acta Math. Sin. (Engl. Ser.) 27(4), 701–714 (2011)CrossRef
  11.M. Bača, M. Miller, O. Phanalasy, A. Semaničová-Feňovčíková, Super d-antimagic labelings of disconnected plane graphs. Acta Math. Sin. (Engl. Ser.) 26(12), 2283–2294 (2010)CrossRef
  12.M. Bača, M. Numan, A. Shabbir, Labelings of type \((1, 1, 1)\) for toroidal fullerenes. Turk. J. Math. 37, 899–907 (2013)
  13.M. Deza, P.W. Fowler, A. Rassat, K.M. Rogers, Fullerenes as tilings of surfaces. J. Chem. Inf. Comput. Sci. 40, 550–558 (2000)CrossRef
  14.D.J. Klein, Elemental benzenoids. J. Chem. Inf. Comput. Sci. 34, 453–459 (1994)CrossRef
  15.D. Ye, H. Zhang, \(2\) -extendability of toroidal polyhexes and Klein bottle polyhexes. Discrete Appl. Math. 157(2), 292–299 (2009)CrossRef
  16.D.J. Klein, H. Zhu, Resonance in elemental benzenoids. Discrete Appl. Math. 67, 157–173 (1996)CrossRef
  17.T.G. Schmalz, W.A. Seitz, D.J. Klein, G.E. Hite, Elemental carbon cages. J. Am. Chem. Soc. 110, 1113–1127 (1988)CrossRef
  18.D. Ye, Z. Qi, H. Zhang, \(k\) -resonant fullerene grpahs. SIAM J. Discrete Math. 23(2), 1023–1044 (2009)CrossRef
  19.D. Ye, H. Zhang, Extrema fullerene graphs with the maximum Clar number. Discrete Appl. Math. 157(14), 3152–3173 (2009)CrossRef
  20.W.C. Shiu, P.C.B. Lam, H. Zhang, \(k\) -resonance in toroidal polyhexes. J. Math. Chem. 38(4), 451–466 (2005)CrossRef
  21.W.C. Shiu, H. Zhang, A complete characterization for \(k\) -resonant Klein-bottle polyhexes. J. Math. Chem. 43(1), 45–59 (2008)CrossRef
  
• 作者单位：Saad Ihsan Butt (1)
  Muhammad Numan (2)
  Shahid Qaisar (3)
  
  1. Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan
  2. Department of Mathematics, Islamia College University, Peshawar, Pakistan
  3. Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal, Pakistan
  
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

In this paper we deal with the problem of labeling the vertices, edges and faces of a Klein bottle fullerenes \({\mathbb {K}}_m^n\) with mn hexagons by the consecutive integers from 1 up to \(|V ({\mathbb {K}}_m^n)|\) + \(|E ({\mathbb {K}}_m^n)|\) + \(|F ({\mathbb {K}}_m^n)|\) in such a way that the label of a 6-sided face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face-weights then form an arithmetic progression with common difference d. The paper examines the existence of such labelings for several differences d.