Year 2020, Volume 49 , Issue 1, Pages 136 - 146 2020-02-06

On topological properties of some convex polytopes by using line operator on their subdivisions

Fatima ASİF [1] , Zohaib ZAHİD [2] , Sohail ZAFAR [3] , Mohammad R. FARAHANİ [4] , Wei GAO [5]


In this paper, we give theoretical results for some topological indices such as Zagreb indices $M_{1}(G)$, $M_{2}(G)$, $M_{3}(G)$, $R(G)$, $M_{1}(\overline{G})$, $M_{2}(\overline{G})$, Zagreb coindices $\overline{M_{1}}(G)$, $\overline{M_{2}}(G)$, $\overline{M_{2}}(\overline{G})$ hyper-Zagreb index $HM(G)$,atom-bond connectivity index $ABC(G)$, sum connectivity index $\chi(G)$ and geometric-arithmetic connectivity index $GA(G)$, by considering $G$ as line graph of subdivision of some convex polytopes and $\overline{G}$ denotes its complement.
Topological indices, line graph, subdivision, convex polytopes
  • [1] M.O. Alberton, The irregularity of a graph, Ars Combin. 46, 219–225, 1997.
  • [2] M. Baca, Labellings of two classes of convex polytopes, Util. Math. 34, 24–31, 1988.
  • [3] M. Baca, On magic labellings of convex polytopes, Ann. Discrete Math. 51, 13–16, 1992.
  • [4] S.H. Bertz, The bond graph, J. C. S. Chem. Commun. 818–820, 1981.
  • [5] B. Bollobas and P. Erdös, Graphs of extremal weights, Ars Combin. 50, 225-233, 1998.
  • [6] K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52, 103–112, 2004.
  • [7] E. Estrada, L. Torres, L. Rodriguez and I. Gutman, An atom-bond connectivity index, Modelling the enthalpy of formation of alkanes, Indian J. Chem. 37, 849–855, 1998.
  • [8] G.H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 65, 79–84, 2011.
  • [9] B. Grünbaum, Graduate text in mathematics convex polytopes, Springer-Verlag, New York, 2003.
  • [10] I. Gutman, Selected properties of the schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34, 1087–1089, 1994.
  • [11] I. Gutman, Edge versions of topological indices, in: Novel Molecular Structure De- scriptors - Theory and Applications II , Univ. Kragujevac, Kragujevac, 2010.
  • [12] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 83–92, 2004.
  • [13] I. Gutman and E. Estrada, Topological indices based on the line graph of the molec- ular graph, J. Chem. Inf. Comput. Sci. 36, 541–543, 1996.
  • [14] I. Gutman and Z. Tomovic, On the application of line graphs in quantitative structure-property studies, J. Serb. Chem. Soc. 65 (8), 577–580, 2000.
  • [15] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total -electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, 535–538, 1972.
  • [16] I. Gutman, B. Furtula, A.A. Toropov and A.P. Toropova, The graph of atomic or- bitals and its basic properties. 2. Zagreb indices, MATCH Commun. Math. Comput. Chem. 53, 225–230, 2005.
  • [17] I. Gutman, B. Furtula, Z.K. Vuki´cevi´c and G. Popivoda, On Zagreb Indices and Coindices, MATCH Commun. Math. Comput. Chem. 74, 5–16, 2015.
  • [18] I. Gutman, L. Popovic, B.K. Mishra, M. Kaunar, E. Estrada and N. Guevara, Ap- plication of line graphs in physical chemistry. Predicting surface tension of alkanes, J. Serb. Chem. Soc. 62, 1025–1029, 1997.
  • [19] P. Hansen, H. Melot and I. Gutman, Variable neighborhood search for extremal graphs 12. A note on the variance of bounded degrees in graphs, MATCH Commun. Math. Comput. Chem. 54, 221–232, 2005.
  • [20] M. Imran, A.Q. Baig and A. Ahmed, Families of plane graphs with constant metric dimension, Util. Math. 88, 43–57, 2012.
  • [21] M. Imran, A.Q. Baig and M.K. Shafiq, Classes of convex polytopes with constant metric dimension, Util. Math. 90, 85-99, 2013.
  • [22] A. Iranmanesh, I. Gutman, O. Khormali and A. Mahmiani, The edge versions of the Wiener index, MATCH Comm. Math. Comput. Chem. 61, 663–672, 2009.
  • [23] M. Randic, On Characterization of Molecular Branching, J. Amer. Chem. Soc. 97, 6609–6615, 1975.
  • [24] M.F. Nadeem, S. Zafar and Z. Zahid, On certain Topological indices of the line graph of subdivision graphs, Appl. Math. Comput. 271, 790–794, 2015.
  • [25] M.F. Nadeem, S. Zafar and Z. Zahid, On Topological properties of the line graphs of subdivision graphs of certain nanostructures, Appl. Math. Comput. 273, 125–130, 2016.
  • [26] M.F. Nadeem, S. Zafar and Z. Zahid, Some Topological Indices of L(S(CNCk[n]), Punjab Univ. J. Math. (Lahore), 49 (1), 13–17, 2017.
  • [27] G.H. Shirdel, H. Rezapour and A.M. Sayadi, The hyper-Zagreb index of graph oper- ations, Iran. J. Math. Chem. 4 (2), 213–220, 2013.
  • [28] H. Van de Waterbeemd, R.E. Carter, G. Grassy, H. Kubiny, Y.C. Martin, M.S. Tutte, and P. Willet, Glossary of terms used in computational drug design, Pure Appl. Chem. 69, 1137–1152, 1997.
  • [29] D. Vukicevic and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46, 1369–1376, 2009.
  • [30] B. Zhou, Zagreb indices, MATCH Commun. Math. Comput. Chem. 52, 113–118, 2004.
  • [31] B. Zhou and N. Trinajstic, On general sum-connectivity index, J. Math. Chem. 47, 210–218, 2010.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-5459-9923
Author: Fatima ASİF
Institution: University of Management and Technology
Country: Pakistan


Orcid: 0000-0003-3797-7029
Author: Zohaib ZAHİD
Institution: University of Management and Technology
Country: Pakistan


Orcid: 0000-0002-8177-7799
Author: Sohail ZAFAR
Institution: University of Management and Technology
Country: Pakistan


Orcid: 0000-0003-2969-4280
Author: Mohammad R. FARAHANİ
Institution: Iran University of Science and Technology
Country: Iran


Orcid: 0000-0001-8744-9334
Author: Wei GAO
Institution: Yunnan Normal University
Country: China


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms535415, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {136 - 146}, doi = {10.15672/HJMS.2019.671}, title = {On topological properties of some convex polytopes by using line operator on their subdivisions}, key = {cite}, author = {ASİF, Fatima and ZAHİD, Zohaib and ZAFAR, Sohail and FARAHANİ, Mohammad R. and GAO, Wei} }
APA ASİF, F , ZAHİD, Z , ZAFAR, S , FARAHANİ, M , GAO, W . (2020). On topological properties of some convex polytopes by using line operator on their subdivisions. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 136-146 . DOI: 10.15672/HJMS.2019.671
MLA ASİF, F , ZAHİD, Z , ZAFAR, S , FARAHANİ, M , GAO, W . "On topological properties of some convex polytopes by using line operator on their subdivisions". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 136-146 <https://dergipark.org.tr/en/pub/hujms/issue/52287/535415>
Chicago ASİF, F , ZAHİD, Z , ZAFAR, S , FARAHANİ, M , GAO, W . "On topological properties of some convex polytopes by using line operator on their subdivisions". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 136-146
RIS TY - JOUR T1 - On topological properties of some convex polytopes by using line operator on their subdivisions AU - Fatima ASİF , Zohaib ZAHİD , Sohail ZAFAR , Mohammad R. FARAHANİ , Wei GAO Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2019.671 DO - 10.15672/HJMS.2019.671 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 136 EP - 146 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.671 UR - https://doi.org/10.15672/HJMS.2019.671 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On topological properties of some convex polytopes by using line operator on their subdivisions %A Fatima ASİF , Zohaib ZAHİD , Sohail ZAFAR , Mohammad R. FARAHANİ , Wei GAO %T On topological properties of some convex polytopes by using line operator on their subdivisions %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2019.671 %U 10.15672/HJMS.2019.671
ISNAD ASİF, Fatima , ZAHİD, Zohaib , ZAFAR, Sohail , FARAHANİ, Mohammad R. , GAO, Wei . "On topological properties of some convex polytopes by using line operator on their subdivisions". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 136-146 . https://doi.org/10.15672/HJMS.2019.671
AMA ASİF F , ZAHİD Z , ZAFAR S , FARAHANİ M , GAO W . On topological properties of some convex polytopes by using line operator on their subdivisions. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 136-146.
Vancouver ASİF F , ZAHİD Z , ZAFAR S , FARAHANİ M , GAO W . On topological properties of some convex polytopes by using line operator on their subdivisions. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 146-136.