Journal of Mathematical Chemistry

, Volume 57, Issue 4, pp 1053–1074 | Cite as

Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectors

  • Juan Alberto Rodríguez-VelázquezEmail author
  • Alexandru T. Balaban
Original Paper


The Estrada topological index EE, based on the eigenvalues of the adjacency matrix, is degenerate for cospectral graphs. By additionally considering the eigenvectors, two new topological indices are devised, which have reduced degeneracy for alkanes or cyclic graphs. Index \( RV_{a} \) shows similarity to EE in ordering of alkanes with 8–10 carbon atoms, whereas index \( RV_{b} \) is more similar to the average distance-based connectivity (Balaban index J). Inter-correlations between these four topological indices are discussed, indicating which factors have predominant influence.


Topological index Balaban index Estrada index Graph eigenvalues 



The first author of this paper thanks Prof. Douglas J. Klein, who invited him for a research stay at Texas A&M University at Galveston in 2018. The results included in this paper were obtained there. This research was supported in part by the Spanish government under the Grants MTM2016-78227-C2-1-P and PRX17/00102.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliTarragonaSpain
  2. 2.Foundational SciencesTexas A&M University at GalvestonGalvestonUSA

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