SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 6

Labelings of type (1, 1, 1) for toroidal fullerenes

Martin BACA
Muhammad NUMAN
Ayesha SHABBIR
Pages
899–907
Publication Date
2022-11-05
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The paper examines the existence of such labelings for several differences d .

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene $Bbb{H} ^n_m$ with mn hexagons by the consecutive integers from 1 up to |V $Bbb({H} ^n_m)$| + |E$Bbb({H} ^n_m)$| + |F $Bbb({H} ^n_m)$| in such a way that the set of face-weights of 6 -sided faces forms an arithmetic progression with common difference d , where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face.
📊
Key Findings & Data:In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene $Bbb{H} ^n_m$ with mn hexagons by the consecutive integers from 1 up to |V $Bbb({H} ^n_m)$| + |E$Bbb({H} ^n_m)$| + |F $Bbb({H} ^n_m)$| in such a way that the set of face-weights of 6 -sided faces forms an arithmetic progression with common difference d , where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face.
💡
Conclusion & Impact:The paper examines the existence of such labelings for several differences d .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene $Bbb{H} ^n_m$ with mn hexagons by the consecutive integers from 1 up to |V $Bbb({H} ^n_m)$| + |E$Bbb({H} ^n_m)$| + |F $Bbb({H} ^n_m)$| in such a way that the set of face-weights of 6 -sided faces forms an arithmetic progression with common difference d , where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face. The paper examines the existence of such labelings for several differences d .

🔖

Cite This Article

BACA, M., NUMAN, M., SHABBIR, A. (2022). Labelings of type (1, 1, 1) for toroidal fullerenes. Turkish Journal of Mathematics, Cilt: 37 - Sayı: 6, 899–907. https://ajindex.com/articles/608308

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Ali, G., Baca, M., Bashir, F., Semanicova-Fenovcikova, A.: On face antimagic labelings of disjoint union of prisms. Utilitas Math. 85, 97–112 (2011)
  2. Baca, M.: On magic labelings of grid graphs. Ars Combin. 33, 295–299 (1992)
  3. Baca, M.: On magic labelings of honeycomb. Discrete Math. 105, 305–311 (1992)
  4. Baca, M., Bashir, F., Semanicov ́, A.: Face antimagic labelings of antiprisms. Utilitas Math. 84, 209–224 (2011)
  5. Baca, M., Brankovic, L., Semanicova-Fenovcika, A.: Labelings of plane graphs containing Hamilton path. Acta Math. Sin. 27, 701–714 (2011)
  6. Baca, M., Jendrol S., Miller, M., Ryan, J.: Antimagic labelings of generalized Petersen graphs that are plane. Ars Combin. 73, 115–128 (2004)
  7. Baca, M., Baskoro, E.T., Jendrol S., Miller, M.: Antimagic labelings of hexagonal planar maps. Utilitas Math. 66, 231–238 (2004)
  8. Baca, M., Lin, Y., Miller, M.: Antimagic labelings of grids. Utilitas Math. 72, 65–75 (2007)
  9. Baca, M., Miller, M.: On d -antimagic labelings of type (1, 1, 1) for prisms. J. Combin. Math. Combin. Comput. 44, 199–207 (2003)
  10. Baca, M., Miller, M., Phanalasy, O., Semanicova-Fenovcikova, A.: Super d -antimagic labelings of disconnected plane graphs. Acta Math. Sin. 26, 2283–2294 (2010)
  11. Deza, M., Fowler, P.W., Rassat, A., Rogers, K.M.: Fullerenes as tilings of surfaces. J. Chem. Inf. Comput. Sci. 40, 550–558 (2000)
  12. Lih, K.W.: On magic and consecutive labelings of plane graphs. Utilitas Math. 24, 165–197 (1983)
  13. Klein, D.J.: Elemental benzenoids. J. Chem. Inf. Comput. Sci. 34, 453–459 (1994)
  14. Klein, D.J., Zhu, H.: Resonance in elemental benzenoids. Discrete Appl. Math. 67, 157–173 (1996)
  15. Schmalz, T.G., Seitz, W.A., Klein, D.J., Hite, G.E.: Elemental carbon cages. J. Am. Chem. Soc. 110, 1113–1127 (1988)
  16. Ye, D., Qi, Z., Zhang, H.: On k-resonant fullerene graphs. SIAM J. Discrete Math. 23, 1023–1044 (2009)
  17. Ye, D., Zhang, H.: 2-extendability of toroidal polyhexes and Klein-bottle polyhexes. Discrete Appl. Math. 157, 292–299 (2009)
  18. Ye, D., Zhang, H.: Extremal fullerene graphs with the maximum Clar number. Discrete Appl. Math. 157, 3152–3173 (2009).