Total Irregularity Strengths of a Disjoint Union of (4,6)-Fullerene Graphs

References

• A. T. Balaban, Ed, Chemical Applications of Graph Theory (London: Academic Press, 1967).
   Google Scholar
• A. T. Balaban, “Applications of Graph Theory in Chemistry,” Journal of Chemical Information and Computer Sciences 25, no. 3 (1985): 334–43. doi:10.1021/ci00047a033.
   Google Scholar
• M. Bača, S. Jendrol’, M. Miller, and J. Ryan, “On Irregular Total Labellings,” Discrete Mathematics 307, no. 11–12 (2007): 1378–88. doi:10.1016/j.disc.2005.11.075.
   Web of Science ®Google Scholar
• J. Przybyło, “Linear Bound on the Irregularity Strength and the Total Vertex Irregularity Strength of Graphs,” SIAM Journal on Discrete Mathematics 23, no. 1 (2009): 511–6. doi:10.1137/070707385.
   Web of Science ®Google Scholar
• M. Anholcer, M. Kalkowski, and J. Przybyło, “A New Upper Bound for the Total Vertex Irregularity Strength of Graphs,” Discrete Mathematics 309, no. 21 (2009): 6316–7. doi:10.1016/j.disc.2009.05.023.
   Web of Science ®Google Scholar
• P. Majerski, and J. Przybyło, “Total Vertex Irregularity Strength of Dense Graphs,” Journal of Graph Theory 76, no. 1 (2014): 34–41. doi:10.1002/jgt.21748.
   Web of Science ®Google Scholar
• A. Ahmad, K. M. Awan, and I. Javaid Slamin, “Total Vertex Irregularity Strength of Wheel Related Graphs,” The Australasian Journal of Combinatorics 51 (2011): 147–56.
   Google Scholar
• O. Al-Mushayt, A. Arshad, and M. K. Siddiqui, “Total Vertex Irregularity Strength of Convex Polytope Graphs,” Acta Mathematica Universitatis Comenianae 82, no. 1 (2013): 29–37.
   Google Scholar
• Nurdin, E., T. Baskoro, A. N. M. Salman, and N. N. Goas, “On the Total Vertex Irregularity Strength of Trees,” Discrete Mathematics 310 (2010): 3043–8. doi:10.1016/j.disc.2010.06.041.
   Web of Science ®Google Scholar
• J. Ivančo, and S. Jendrol, “Total Edge Irregularity Strength of Trees,” Discussiones Mathematicae Graph Theory 26, no. 3 (2006): 449–56. doi:10.7151/dmgt.1337.
   Google Scholar
• A. Ahmad, M. Bača, and Y. Bashir, and M. K. Siddiqui, “Total Edge Irregularity Strength of Strong Product of Two Paths,” Ars Combinatoria 106 (2012): 449–59.
   Web of Science ®Google Scholar
• A. Ahmad, M. Bača, and M. K. Siddiqui, “On Edge Irregular Total Labeling of Categorical Product of Two Cycles,” Theory of Computing Systems 54, no. 1 (2014): 1–12. doi:10.1007/s00224-013-9470-3.
   Web of Science ®Google Scholar
• O. Al-Mushayt, A. Ahmad, and M. K. Siddiqui, “On the Total Edge Irregularity Strength of Hexagonal Grid Graphs,” The Australasian Journal of Combinatorics 53 (2012): 263–71.
   Google Scholar
• M. Anholcer, and C. Palmer, “Irregular Labellings of Circulant Graphs,” Discrete Mathematics. 312, no. 23 (2012): 3461–6. doi:10.1016/j.disc.2012.06.017.
   Web of Science ®Google Scholar
• S. Jendrol’, J. Miškuf, and R. Soták, “Total Edge Irregularity Strength of Complete Graphs and Complete Bipartite Graphs,” Discrete Mathematics 310, no. 3 (2010): 400–7. doi:10.1016/j.disc.2009.03.006.
   Web of Science ®Google Scholar
• M. K. M. Haque, “Irregular Total Labelings of Generalized Petersen Graphs,” Theory of Computing Systems 50, no. 3 (2012): 537–44. doi:10.1007/s00224-011-9350-7.
   Web of Science ®Google Scholar
• R. Ramdani, A. N. M. Salman, H. Assiyatum, A. Semaničová-Feňovčíková, and M. Bača, “On the Total Irregularity Strength of Disjoint Union of Arbitrary Graphs,” Mathematical Reports 18 (2016): 469–82.
   Web of Science ®Google Scholar
• H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, “C60: Buckminsterfullerene,” Nature 318, no. 6042 (1985): 162–3. doi:10.1038/318162a0.
   Web of Science ®Google Scholar
• J. An, L. H. Gan, X. Fan, and F. Pan, “Fullerene C46: An Unexpected Non-Classical Cage,” Chemical Physics Letters 511, no. 4–6 (2011): 351–5. doi:10.1016/j.cplett.2011.06.053.
   Google Scholar
• U. H. F. Bunz, Y. Rubish, and Y. Tobe, “Polyethnylated Cyclic π− Systems: Scaffoldings for Novel Two and Three-Dimensional Carbon Networks,” Chemical Society Reviews 28 (1999): 107–19.
   Web of Science ®Google Scholar
• M. V. Diudea, A. E. Vizitiu, T. Beu, A. Bende, C. L. Nagy, and D. Jane, “Circulene Covered Fullerenes,” Journal of Molecular Structure: Theochem 904, no. 1–3 (2009): 28–34. doi:10.1016/j.theochem.2009.02.024.
   Web of Science ®Google Scholar
• H. Prinzbach, A. Weller, and P. Landenberger, “Gas-Phase Production and Photoelectron Spectroscopy of the Smallest Fullerene, C20,” Nature 407, no. 6800 (2000): 60–3. doi:10.1038/35024037.
   PubMedGoogle Scholar
• D. Sundholm, “C72: Gaudiene, a Hollow and Aromatic All-Carbon Molecule,” Physical Chemistry Chemical Physics 15, no. 23 (2013): 9025–8. doi:10.1039/c3cp51042e.
   Google Scholar
• A. Fonari, J. R. H. Shen, T. Timofeeva, and K. Vollhardt, “Toward Antikekulene: Angular 1,2-Di, 2,3-Di, and 1,2,15,16-Tetrachloro[6]Phenylene,” Synlett 25, no. 17 (2014): 2429–33.
   Web of Science ®Google Scholar
• A. R. Ashrafi, and Z. Mehranian, “Topological Study of (3,6)- and (4,6)-Fullerenes, in Toplogical Modelling of Nanostructures and Extended Systems,” Carbon Materials: Chemistry and Physics, vol. 7 (Berlin, Germany: Springer, 2013), 487–510.
   Google Scholar
• H. Lu, and S. D. Li, “Two-Dimensional Carbon Allotropes from Graphene to Graphyne,” Journal of Materials Chemistry C 1, no. 23 (2013): 3677–80. doi:10.1039/c3tc30302k.
   Web of Science ®Google Scholar
• X. L. Sheng, H. J. Cui, F. Ye, Q. B. Yan, Q. R. Zheng, and G. Su, “Octagraphene as a Versatile Carbon Atomic Sheet for Novel Nanotubes, Unconventional Fullerenes, and Hydrongen Storage,” Journal of Applied Physics 112, no. 7 (2012): 074315. doi:10.1063/1.4757410.
   Web of Science ®Google Scholar
• Q. Song, B. Wang, K. Deng, X. Feng, M. Wagner, J. D. Gale, K. Müllen, and L. Zhi, “Grapheneylene, a Unique Two-Dimensional Carbon Network with Nondelocalized Cyclohexatriene Units,” Journal of Materials Chemistry C 1, no. 1 (2013): 38–41. doi:10.1039/C2TC00006G.
   Web of Science ®Google Scholar
• W. W. Wang, J. S. Dang, and X. Zhao, “Impact of Tetragonal Rings on the Stability of Small Fullerenes Encapsulated with Noble Gas: A Density Functional Theory Survey,” Chemical Physics Letters 536 (2012): 77–81. doi:10.1016/j.cplett.2012.03.055.
   Web of Science ®Google Scholar
• Z. Wei, and H. Zhang, “Number of Matchings of Low Order in (4,6)-Fullerene Graphs,” MATCH Communications in Mathematical and in Computer Chemistry 77 (2017): 707–24.
   Web of Science ®Google Scholar