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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

On the degree locating indices of graphs

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pp. 255–269Vol. 26Issue 1February 2021DOI: 10.1080/09720529.2021.1936898 Crossmark XML
Received:
31 Oct 2020
Accepted:
31 Mar 2021
Published Online:
15 Nov 2021
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1355
Pages:
255–269

Abstract

Graph theory has supported chemists with topological indices which predict different physicochemical properties such as boiling point, entropy, acentric factor, etc. of chemical compounds. In this article, we introduce two new topological indices called degree locating indices, based on the degree and location of the vertices. We present exact expressions for some families of standard graphs and we get the exact values of these indices for any graph of diameter two. Finally, we compute these indices for join graphs and book graphs.

Keywords

Zagreb indicesFirst and second locating indicesJoin graph

Subject Classifications

05C0505C1205C90

References

  1. A. Alwardi, A. Alqesmah, R. Rangarajan and I.N. Cangul, Entire Zagreb Indices of Graphs, Discrete Math. Algorithm. Appl., 10 (3) (2018) 1850037 (16 pages). doi: https://doi.org/10.1142/S1793830918500374 [Crossref], [Web of Science ®], [Google Scholar]
  2. J. Braun, A. Kerber, M. Meringer, C. Rucker, Similarity of molecular descriptors: the equivalence of Zagreb indices and walk counts, MATCH Commun. Math. Comput. Chem. 54 (2005) 163-176. [Web of Science ®], [Google Scholar]
  3. G. Chartand, L. Lesniak, Graphs and Digraphs, 4th ed., Boca Raton, FL, USA: CRC Press, 2005. [Google Scholar]
  4. K.C. Das, A. Yurttas, M. Togan, A.S. Cevik, I.N. Cangul, The multiplicative Zagreb indices of graph operation, Journal of inequalities and applications, 2013 (1), 90. [Google Scholar]
  5. M.V. Diudea, M.S. Florescu, P.V. Khadikar, Molecular Topolgy and Its Applications, Eficon, Bucarest, 2006. [Google Scholar]
  6. M.V. Diudea, Nanomolecules and Nanostructures-Poynomial and Indices, Univ. Kragujevac, 2010. [Google Scholar]
  7. I. Gutman, B. Furula (Eds.), Distance in Molecular Graphs, Univ. Kragujevac, Kragujevac, 2012. [Google Scholar]
  8. I. Gutman, B. Furula (Eds.), Novel Molecular Structure Descriptors- Theory and Applications I, Univ. Kragujevac, Kragujevac, 2010. [Google Scholar]
  9. I. Gutman, B. Furula (Eds.), Novel Molecular Structure Descriptors- Theory and Applications II, Univ. Kragujevac, Kragujevac, 2010. [Google Scholar]
  10. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals, Total p - electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538. doi: https://doi.org/10.1016/0009-2614(72)85099-1 [Crossref], [Web of Science ®], [Google Scholar]
  11. I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92. [Google Scholar]
  12. M. Karelson, Molecular Descriptors in QSAR-QSPR, Wiley, New York, 2000. [Google Scholar]
  13. M. H. Khalifeh, H. Youse -Azari, A.R. Ashra, The first and second Zagreb indices of some graph operations, Discrete Applied Mathematics 157 (2009) 804-811. doi: https://doi.org/10.1016/j.dam.2008.06.015 [Crossref], [Web of Science ®], [Google Scholar]
  14. J.X. Li, J.M. Guo and W.C. Shiu, On the Second Largest Laplacian Eignvalues of Graphs, Linear Algebra Appl., 438 (2013) 2438-2446. doi: https://doi.org/10.1016/j.laa.2012.10.047 [Crossref], [Web of Science ®], [Google Scholar]
  15. S. Nikolić, G. Kovac̃ević, A. Milic̃ević, N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113-124. [Web of Science ®], [Google Scholar]
  16. K. Pattabiraman and A. Santhakumar, Reformulated Zagreb indices of vertex F-join graphs, Journal of Discrete Mathematical Sciences and Cryptography, 23:3, (2020) 759-772, DOI: https://doi.org/10.1080/09720529.2019.1681672. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  17. H.N. Ramaswamy, A. Alwardi, N.R. Kumar, On the locating matrix of a graph and its spectral analysis. Computer Science Journal of Moldova, vol. 25, no. 3(75), 2017. [Google Scholar]
  18. R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000. 
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