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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Topological indices · line graph · subdivision
Abstract
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.
ASİF, F., ZAHİD, Z., ZAFAR, S., FARAHANİ, M. R., GAO, W. (2020). On topological properties of some convex polytopes by using line operator on their subdivisions. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 136–146. https://ajindex.com/articles/669299
M.O. Alberton, The irregularity of a graph, Ars Combin. 46, 219–225, 1997
M. Baca, Labellings of two classes of convex polytopes, Util. Math. 34, 24–31, 1988
M. Baca, On magic labellings of convex polytopes, Ann. Discrete Math. 51, 13–16, 1992
S.H. Bertz, The bond graph, J. C. S. Chem. Commun. 818–820, 1981
B. Bollobas and P. Erdös, Graphs of extremal weights, Ars Combin. 50, 225-233, 1998
K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52, 103–112, 2004
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
G.H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 65, 79–84, 2011
B. Grünbaum, Graduate text in mathematics convex polytopes, Springer-Verlag, New York, 2003
I. Gutman, Selected properties of the schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34, 1087–1089, 1994
I. Gutman, Edge versions of topological indices, in: Novel Molecular Structure De- scriptors - Theory and Applications II, Univ. Kragujevac, Kragujevac, 2010
I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 83–92, 2004
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
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
I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total -electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, 535–538, 1972
I. Gutman, B. Furtula, A.A. Toropov and A.P. Toropova, The graph of atomic or- bitals and its basic properties
Zagreb indices, MATCH Commun. Math. Comput. Chem. 53, 225–230, 2005
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
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
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