Remark on Forgotten Topological Index of a Line Graph
Abstract
Let G be a simple connected graph with n vertices and m edgesand let d(e1) > d(e2) > > d(em) be edge degree sequence of graph G.
Denote by EF = Σm i=1 d(ei)3 reformulated forgotten index of G. Lower and upper bounds for the invariant EF are obtained.
References
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[2] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman. Zagreb indices: Bounds and Extremal graphs. In: I. Gutman, B. Furtula, K. C. Das, E. Milovanovic and I. Milovanovic (Eds.) Bounds in Chemical Graph Theory { Basics (pp. 67-153), Mathematical Chemistry Monographs, MCM 19, Univ. Kragujevac, Kragujevac, 2017.
[3] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman. Bounds for Zagreb indices. MATCH Commun. Math. Comput. Chem., 78(1)(2017), 17-100.
[4] P. Cerone and S. S. Dragomir. A refiment of the Gruss inequality and applications. Tamkang J. Math., 38(1)(2007), 34-49.
[5] T. Doslic, B. Furtula, A. Graovac, I. Gutman, S. Moradi and Z. Yarahmadi. On vertex{ degree{based molecular structure descriptors. MATCH Commun. Math. Comput. Chem.,
66(2)(2011), 613-626.
[6] B. Furtula and I. Gutman. A forgotten topological index. J. Math. Chem., 53(4)(2015), 1184-1190.
[7] I. Gutman and N. Trinajstic. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 17(4)(1972), 535-538.
[8] I. Gutman. On the origin of two degree-based topological indices. Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.), 146(2014), 39-52.
[9] I. Gutman. Degree-based topological indices. Croat. Chem. Acta, 86(4)(2013), 351-361.
[10] I. Gutman and K. C. Das. The First Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem., 50(2004), 83{92.
[11] I. Gutman, B. Furtula, Z. Kovijanic Vukicevic and G. Popivoda. On Zagreb indices and coindices. MATCH Commun. Math. Comput. Chem., 74(1)(2015), 5-16.
[12] V. R. Kuli. On edge index and coindex of graphs. Inter. J. Fuzzy Math. Arh., 10(2)(2016), 111-116.
[13] A. Lupas. A remark on the Schweitzer and Kantorovich inequalities. Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 381-409 (1972), 13-15.
[14] A. Milicevic, S. Nikolic and N. Trinajstic. On reformulated Zagreb indices. Mol. Divers., 8(4)(2004), 393-399.
[15] E. I. Milovanovic, I. Z. Milovanovic, E. C. Dolicanin and E. Glogic. A note on the First reformulated Zagreb index. Appl. Math. Comput., 273(2016), 16-20.
[16] I. Z. Milovanovic, E. I. Milovanovic, I. Gutman and B. Furtula. Some inequalities for the forgotten topological index. Inter. J. Appl. Graph Theory, 1(1)(2017), 1-15.
[17] D. S. Mitrinovic and P. M. Vasic. Analytic inequalities. Springer Verlag, Berlin-Heidelberg- New York, 1970.
[18] P. M. Vasic and R. Z. Djordjevic. Cebysev inequality for convex sets. Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 412{460 (1973), 17-20.
[19] B. Zhou and N. Trinajstic. On a novel connectivity index. J. Math. Chem., 46(4)(2009), 1252-1270.
[2] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman. Zagreb indices: Bounds and Extremal graphs. In: I. Gutman, B. Furtula, K. C. Das, E. Milovanovic and I. Milovanovic (Eds.) Bounds in Chemical Graph Theory { Basics (pp. 67-153), Mathematical Chemistry Monographs, MCM 19, Univ. Kragujevac, Kragujevac, 2017.
[3] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman. Bounds for Zagreb indices. MATCH Commun. Math. Comput. Chem., 78(1)(2017), 17-100.
[4] P. Cerone and S. S. Dragomir. A refiment of the Gruss inequality and applications. Tamkang J. Math., 38(1)(2007), 34-49.
[5] T. Doslic, B. Furtula, A. Graovac, I. Gutman, S. Moradi and Z. Yarahmadi. On vertex{ degree{based molecular structure descriptors. MATCH Commun. Math. Comput. Chem.,
66(2)(2011), 613-626.
[6] B. Furtula and I. Gutman. A forgotten topological index. J. Math. Chem., 53(4)(2015), 1184-1190.
[7] I. Gutman and N. Trinajstic. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 17(4)(1972), 535-538.
[8] I. Gutman. On the origin of two degree-based topological indices. Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.), 146(2014), 39-52.
[9] I. Gutman. Degree-based topological indices. Croat. Chem. Acta, 86(4)(2013), 351-361.
[10] I. Gutman and K. C. Das. The First Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem., 50(2004), 83{92.
[11] I. Gutman, B. Furtula, Z. Kovijanic Vukicevic and G. Popivoda. On Zagreb indices and coindices. MATCH Commun. Math. Comput. Chem., 74(1)(2015), 5-16.
[12] V. R. Kuli. On edge index and coindex of graphs. Inter. J. Fuzzy Math. Arh., 10(2)(2016), 111-116.
[13] A. Lupas. A remark on the Schweitzer and Kantorovich inequalities. Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 381-409 (1972), 13-15.
[14] A. Milicevic, S. Nikolic and N. Trinajstic. On reformulated Zagreb indices. Mol. Divers., 8(4)(2004), 393-399.
[15] E. I. Milovanovic, I. Z. Milovanovic, E. C. Dolicanin and E. Glogic. A note on the First reformulated Zagreb index. Appl. Math. Comput., 273(2016), 16-20.
[16] I. Z. Milovanovic, E. I. Milovanovic, I. Gutman and B. Furtula. Some inequalities for the forgotten topological index. Inter. J. Appl. Graph Theory, 1(1)(2017), 1-15.
[17] D. S. Mitrinovic and P. M. Vasic. Analytic inequalities. Springer Verlag, Berlin-Heidelberg- New York, 1970.
[18] P. M. Vasic and R. Z. Djordjevic. Cebysev inequality for convex sets. Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 412{460 (1973), 17-20.
[19] B. Zhou and N. Trinajstic. On a novel connectivity index. J. Math. Chem., 46(4)(2009), 1252-1270.
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Published
2017-04-13
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