New Bounds for Zagreb Eccentricity Indices

Author(s)
Nilanjan De

Affiliation(s)

Department of Basic Science and Humanities (Mathematics), Calcutta Institute of Engineering and Management, Kolkata, India.

Department of Basic Science and Humanities (Mathematics), Calcutta Institute of Engineering and Management, Kolkata, India.

ABSTRACT

The Zagrebeccentricity indices are the eccentricity version of the classical Zagrebindices. The first Zagrebeccentricity index (*E*_{1}(*G*)) is defined as sum of squares of the eccentricities of the vertices and the second Zagrebeccentricity index (*E*_{2}(*G*)) is equal to sum of product of the eccentricities of the adjacent vertices. In this paper we give some new upper and lower bounds for first and second Zagreb eccentricity indices.

The Zagrebeccentricity indices are the eccentricity version of the classical Zagrebindices. The first Zagrebeccentricity index (

Cite this paper

N. De, "New Bounds for Zagreb Eccentricity Indices,"*Open Journal of Discrete Mathematics*, Vol. 3 No. 1, 2013, pp. 70-74. doi: 10.4236/ojdm.2013.31014.

N. De, "New Bounds for Zagreb Eccentricity Indices,"

References

[1] P. Dankelmann, W. Goddard and C. S. Swart, “The Average Eccentricity of a Graph and Its Subgraphs,” Utilitas Final Copy, Vol. 65, 2004, pp. 41-51.

[2] I. Gutman and N. Trinajsti?, “Graph Theory and Molecular Orbitals, Total φ-Electron Energy of Alternant Hydrocarbons,” Chemical Physics Letters, Vol. 17, 1972, pp. 535-538. doi:10.1016/0009-2614(72)85099-1

[3] D. Vuki?evi? and A. Graovac, “Note on the Comparison of the First and Second Normalized Zagreb Eccentricity Indices,” Acta Chimica Slovenica, Vol. 57, 2010, pp. 524-528.

[4] M. Ghorbani and M. A. Hosseinzadeh, “A New Version of Zagreb Indices,” Filomat, Vol. 26, No. 1, 2012, pp. 93-100. doi:10.2298/FIL1201093G

[5] R. Xing, B. Zhou and N. Trinajsti?, “On Zagreb Eccentricity Indices,” Croatica Chemica Acta, Vol. 84, No. 4, 2011, pp.493-497. doi:10.5562/cca1801

[6] K. C. Das, D. W. Lee and A. Gravovac, “Some Properties of Zagreb Eccentricity Indices,” Ars Mathematica Contemporanea, Vol. 6, No. 1, 2013, pp. 117-125.

[7] V. Sharma, R. Goswami and A. K. Madan, “Eccentric Connectivity Index: A Novel Highly Discriminating Topological Descriptor for Structure-Property and Structure-Activity Studies,” Journal of Chemical Information Computer Sciences, 1997, Vol. 37, No. 2, pp. 273-282. doi:10.1021/ci960049h

[8] B. Zhou and Z. Du, “On Eccentric Connectivity Index,” MATCH: Communications in Mathematical and in Computer Chemistry, Vol. 63, No. 1, 2010, pp. 181-198.

[9] N. De, “Eccentric Connectivity Index of Thorn Graph,” Applied Mathematics, Vol. 3, No. 8, 2012, pp. 931-934. doi:10.4236/am.2012.38139

[10] A. Ili? and I. Gutman, “Eccentric Connectivity Index of Chemical Trees,” MATCH: Communications in Mathematical and in Computer Chemistry, Vol. 65, 2011, pp. 731-744.

[11] K.C. Das, “Maximizing the Sum of the Squares of Degrees of a Graph,” Discrete Mathematics, Vol. 285, No. 1-3, 2004, pp. 57-66. doi:10.1016/j.disc.2004.04.007

[12] A. Ili?, M. Ili? and B. Liu, “On the Upper Bounds for the First Zagreb Index,” Kragujevac Journal of Mathematics, Vol. 35, No. 1, 2011, pp. 173-182.

[13] N. De, “Some Bounds of Reformulated Zagreb Indices,” Applied Mathematical Sciences, Vol. 6, No. 101-104, 2012, pp. 5005-5012.

[14] K. Ch. Das, I. Gutman and B. Zhou, “New Upper Bounds on Zagreb Indices,” J. Math. Chem., Vol. 46, No. 2, 2009, pp. 514-521. doi:10.1007/s10910-008-9475-3

[15] N. De, “Bounds for the connective eccentric index,” International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 44, 2012, pp. 2161-2166.

[1] P. Dankelmann, W. Goddard and C. S. Swart, “The Average Eccentricity of a Graph and Its Subgraphs,” Utilitas Final Copy, Vol. 65, 2004, pp. 41-51.

[2] I. Gutman and N. Trinajsti?, “Graph Theory and Molecular Orbitals, Total φ-Electron Energy of Alternant Hydrocarbons,” Chemical Physics Letters, Vol. 17, 1972, pp. 535-538. doi:10.1016/0009-2614(72)85099-1

[3] D. Vuki?evi? and A. Graovac, “Note on the Comparison of the First and Second Normalized Zagreb Eccentricity Indices,” Acta Chimica Slovenica, Vol. 57, 2010, pp. 524-528.

[4] M. Ghorbani and M. A. Hosseinzadeh, “A New Version of Zagreb Indices,” Filomat, Vol. 26, No. 1, 2012, pp. 93-100. doi:10.2298/FIL1201093G

[5] R. Xing, B. Zhou and N. Trinajsti?, “On Zagreb Eccentricity Indices,” Croatica Chemica Acta, Vol. 84, No. 4, 2011, pp.493-497. doi:10.5562/cca1801

[6] K. C. Das, D. W. Lee and A. Gravovac, “Some Properties of Zagreb Eccentricity Indices,” Ars Mathematica Contemporanea, Vol. 6, No. 1, 2013, pp. 117-125.

[7] V. Sharma, R. Goswami and A. K. Madan, “Eccentric Connectivity Index: A Novel Highly Discriminating Topological Descriptor for Structure-Property and Structure-Activity Studies,” Journal of Chemical Information Computer Sciences, 1997, Vol. 37, No. 2, pp. 273-282. doi:10.1021/ci960049h

[8] B. Zhou and Z. Du, “On Eccentric Connectivity Index,” MATCH: Communications in Mathematical and in Computer Chemistry, Vol. 63, No. 1, 2010, pp. 181-198.

[9] N. De, “Eccentric Connectivity Index of Thorn Graph,” Applied Mathematics, Vol. 3, No. 8, 2012, pp. 931-934. doi:10.4236/am.2012.38139

[10] A. Ili? and I. Gutman, “Eccentric Connectivity Index of Chemical Trees,” MATCH: Communications in Mathematical and in Computer Chemistry, Vol. 65, 2011, pp. 731-744.

[11] K.C. Das, “Maximizing the Sum of the Squares of Degrees of a Graph,” Discrete Mathematics, Vol. 285, No. 1-3, 2004, pp. 57-66. doi:10.1016/j.disc.2004.04.007

[12] A. Ili?, M. Ili? and B. Liu, “On the Upper Bounds for the First Zagreb Index,” Kragujevac Journal of Mathematics, Vol. 35, No. 1, 2011, pp. 173-182.

[13] N. De, “Some Bounds of Reformulated Zagreb Indices,” Applied Mathematical Sciences, Vol. 6, No. 101-104, 2012, pp. 5005-5012.

[14] K. Ch. Das, I. Gutman and B. Zhou, “New Upper Bounds on Zagreb Indices,” J. Math. Chem., Vol. 46, No. 2, 2009, pp. 514-521. doi:10.1007/s10910-008-9475-3

[15] N. De, “Bounds for the connective eccentric index,” International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 44, 2012, pp. 2161-2166.