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Year 2018, Volume: 8 Issue: 1, 61 - 70, 01.06.2018

Abstract

References

  • Buckley F. and Harary F., (1990), Distance in Graphs, Addison-Wesley Publishing Company Ad- vanced Book Program, Redwood City, CA.
  • Chartrand G. and Lesniak L., (1986), Graphs and Digraphs, Second Edition, Wadsworth, Monterey.
  • Das K.Ch., (2010), On GeometricArithmetic Index of Graphs, MATCH Commun. Math. Comput. Chem., 64, pp. 619-630.
  • Gutman I. and Trinajstic N., (1972), Graph theory and molecular orbitals. Total Π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535-538.
  • Gutman I. and Furtula B., (2008), Recent Results in the Theory of Randi Index, Univ. Kragujevac, Kragujevac.
  • Gallian J.A., (2016), A dynamic survey of graph labeling, Elect. Jour. Combin., DS6, Nineteenth edition, December 23.
  • Javaid I. and Shokat S., (2008), On the partition dimension of some wheel related graphs, Jour. of Pri. Res. in Math., 4, pp. 154-164.
  • Li X. and Gutman I., (2006), Mathematical Aspects of Randi-Type Molecular Structure Descriptors
  • Univ. Kragujevac, Kragujevac, ISBN: 86-81829-67-X.
  • Mahmiani A., Khormali O. and Iranmanesh A., (2012), On The Edge Version of Geometric-Arithmetic
  • Index, Digest Journal of Nanomaterials and Biostructures, 7(2), pp. 411-414. Nikolic S., Kovacevic G., Milicevic A. and Trinajstic N., (2003), The Zagreb indices 30 years after, Croat. Chem. Acta, 76, pp. 113-124.
  • Randic M., (1975) On characterization of molecular branching, J. Am. Chem. Soc., 97, pp. 6609-6615.
  • Odabas Z.N. and Berberler M.E., (2013), The Edge Geometric-Arithmetic Index of an Infinite Class of Dendrimers, Jour. of Comput. and Theor. Nanosci., 10(9), pp. 2207-2208.
  • Turacı T., (2016), The Average Lower 2-domination Number of Wheels Related Graphs and an Al- gorithm, Math. and Comput. App., 21(3), 29.
  • Turacı T., (2016), Zagreb Eccentricity Indices of Cycles Related Graphs, Ars Combinatoria, 125, pp. 256.
  • Turacı T. and Okten M., (2015), The Edge Eccentric Connectivity Index of Hexagonal Cactus Chains
  • Jour. of Comp. and Theo. Nanosci., 12(10), pp. 3977-3980.
  • Vukicevic D. and Furtula B., (2009), Topological index based on the ratios of geometrical and arith- metical means of end-vertex degrees of edges, J. Math. Chem., 46, pp. 1369-1376.
  • West D.B., (2001), Introduction to Graph Theory, Prentice Hall, NJ.
  • Wiener H., (1947), Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., 69(1), pp. 17-20.

ON ARITHMETIC-GEOMETRIC INDEX GA AND EDGE GA INDEX

Year 2018, Volume: 8 Issue: 1, 61 - 70, 01.06.2018

Abstract

Let G V G ;E G be a simple connected graph and dG u be the degree of the vertex u. Topological indices are numerical parameters of a graph which are invariant under graph isomorphisms. Recently, people are studying various topological measures such as the arithmetic-geometric index and the edge version of arithmetic- geometric index of a graph G. Topological index based on the ratios of geometrical and arithmetical means of end vertex degrees of edges. In this paper, exact values for the arithmetic-geometric index and the edge version of arithmetic-geometric index of wheel related graphs namely gear, helm, sun ower and friendship graph are obtained.

References

  • Buckley F. and Harary F., (1990), Distance in Graphs, Addison-Wesley Publishing Company Ad- vanced Book Program, Redwood City, CA.
  • Chartrand G. and Lesniak L., (1986), Graphs and Digraphs, Second Edition, Wadsworth, Monterey.
  • Das K.Ch., (2010), On GeometricArithmetic Index of Graphs, MATCH Commun. Math. Comput. Chem., 64, pp. 619-630.
  • Gutman I. and Trinajstic N., (1972), Graph theory and molecular orbitals. Total Π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535-538.
  • Gutman I. and Furtula B., (2008), Recent Results in the Theory of Randi Index, Univ. Kragujevac, Kragujevac.
  • Gallian J.A., (2016), A dynamic survey of graph labeling, Elect. Jour. Combin., DS6, Nineteenth edition, December 23.
  • Javaid I. and Shokat S., (2008), On the partition dimension of some wheel related graphs, Jour. of Pri. Res. in Math., 4, pp. 154-164.
  • Li X. and Gutman I., (2006), Mathematical Aspects of Randi-Type Molecular Structure Descriptors
  • Univ. Kragujevac, Kragujevac, ISBN: 86-81829-67-X.
  • Mahmiani A., Khormali O. and Iranmanesh A., (2012), On The Edge Version of Geometric-Arithmetic
  • Index, Digest Journal of Nanomaterials and Biostructures, 7(2), pp. 411-414. Nikolic S., Kovacevic G., Milicevic A. and Trinajstic N., (2003), The Zagreb indices 30 years after, Croat. Chem. Acta, 76, pp. 113-124.
  • Randic M., (1975) On characterization of molecular branching, J. Am. Chem. Soc., 97, pp. 6609-6615.
  • Odabas Z.N. and Berberler M.E., (2013), The Edge Geometric-Arithmetic Index of an Infinite Class of Dendrimers, Jour. of Comput. and Theor. Nanosci., 10(9), pp. 2207-2208.
  • Turacı T., (2016), The Average Lower 2-domination Number of Wheels Related Graphs and an Al- gorithm, Math. and Comput. App., 21(3), 29.
  • Turacı T., (2016), Zagreb Eccentricity Indices of Cycles Related Graphs, Ars Combinatoria, 125, pp. 256.
  • Turacı T. and Okten M., (2015), The Edge Eccentric Connectivity Index of Hexagonal Cactus Chains
  • Jour. of Comp. and Theo. Nanosci., 12(10), pp. 3977-3980.
  • Vukicevic D. and Furtula B., (2009), Topological index based on the ratios of geometrical and arith- metical means of end-vertex degrees of edges, J. Math. Chem., 46, pp. 1369-1376.
  • West D.B., (2001), Introduction to Graph Theory, Prentice Hall, NJ.
  • Wiener H., (1947), Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., 69(1), pp. 17-20.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

- V.aytaç This is me

- T.turacı This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

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