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RELATIONS BETWEEN THE FIRST AND SECOND ZAGREB INDICES OF SUBDIVISION GRAPHS

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초록

The first and second Zagreb indices of a graph are two of the topological invariants used in molecular calculations by Mathematicians and Chemists. First Zagreb index and multiplicative Zagreb indices, all versions of Zagreb indices of subdivision graphs, Zagreb indices of the line graphs of the subdivision graphs, Zagreb indices of subdivision graphs of double graphs, multiplicative Zagreb indices of graph operations were cal- culated and as a generalisation, the authors determined the multiplicative Zagreb indices of the r-subdivision of double graphs. In this paper, we ob- tain numerous new relations between the first and second Zagreb indices of the subdivision graphs of certain graph types.

Abstract

The first and second Zagreb indices of a graph are two of the topological invariants used in molecular calculations by Mathematicians and Chemists. First Zagreb index and multiplicative Zagreb indices, all versions of Zagreb indices of subdivision graphs, Zagreb indices of the line graphs of the subdivision graphs, Zagreb indices of subdivision graphs of double graphs, multiplicative Zagreb indices of graph operations were cal- culated and as a generalisation, the authors determined the multiplicative Zagreb indices of the r-subdivision of double graphs. In this paper, we ob- tain numerous new relations between the first and second Zagreb indices of the subdivision graphs of certain graph types.

참고문헌 (13)

  1. M. Ascioglu, "Sigma Index and Forgotten Index of the Subdivision and r-Subdivision Graphs", Proceedings of the Jangjeon Mathematical Society, 21(2) (2018)
  2. K. Ch. Das, "The multiplicative Zagreb indices of graph operations", Journal of Inequalities and Applications, 90, pp.1~14 (2013)
  3. K. Ch. Das, "On the first Zagreb index and multiplicative Zagreb coindices of graphs", Analele Stiintifice ale Universitatii Ovidius Constanta, 24(1), pp.153~176 (2016)
  4. I. Gutman, "Graph Theory and Molecular Orbitals III, Total <TEX>${\pi}$<", TEX>-electron energy of alternant hydrocarbons, 1972, pp.17, 535~538
  5. B. Horoldagva, "Complete characterization of graphs for direct comparing Zagreb indices", Discrete Appl. Math., 215, pp.146~154 (2016)[DOI]
  6. M. H. Khalifeh, "The First and second Zagreb indices of some graph operations", Discrete Appl Math, 157, pp.804~811 (2009)[DOI]
  7. V. Lokesha, "Computing ABC, GA, Randic and Zagreb Indices", Enlightments of Pure and Applied Mathematics (EPAM), 1(1), pp.17~28 (2015)
  8. M. Milosevic, "On the Constant Difference of Zagreb indices", MATCH Commun. Math. Comput. Chem., 68, pp.157~168 (2012)
  9. P. S. Ranjini, "On the Zagreb indices of the line graphs of the subdivision graphs", Appl Math Comput, 218, pp.699~702 (2011)
  10. M. Togan, "Some formulae and inequalities on several Zagreb indices of r-subdivision graphs", Enlightments of Pure and Applied Mathematics (EPAM), 1(1), pp.29~45 (2015)
  11. Muge TOGAN, "All versions of Zagreb indices and coindices of subdivision graphs of certain graph types", Advanced Studies in Contemporary Mathematics, 26(1), pp.227~236 (2016), 장전수학회
  12. M. Togan, "Zagreb and multiplicative Zagreb indices of r-subdivision graphs of double graphs", Scientia Magna, 12(1), pp.115~119 (2017)
  13. Aysun YURTTAS, "Zagreb indices and multiplicative Zagreb indices of subdivision graphs of double graphs", Advanced Studies in Contemporary Mathematics, 26(3), pp.407~416 (2016), 장전수학회

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