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On the largest eigenvalue of extended eccentric matrix

Author

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  • Ghorbani, Modjtaba
  • Alidehi-Ravandi, Razie
  • Amraei, Najaf
  • Raza, Zahid

Abstract

Following the symmetric division deg index, this article introduces a new graph index called the SDE index which is based on the eccentrity of vertices. Also, the eccentric version of the extended adjacency matrix is defined. We establish several results regarding the properties of the extended eccentric matrix and spectra of different classes of graphs including trees and unicyclic graphs. Some new bounds also for the minimum spectral radius of the extended eccentric matrices were determined. Besides, we present bounds for the extended eccentric spectral radius of path graph and prove that the maximum value of the extended eccentric spectral radius in a tree is attained by the star graph. In our research, we explore the potential applications of the SDE index in chemical graph theory. Our findings illustrate a noteworthy correlation between the SDE index and several physical and chemical properties. This correlation highlights the promising potential of the index as a predictive tool for the molecular behavior of various compounds. For example, the SDE index has a stronger negative correlation with the M1, M2, and M3 indices (r= −0.93, −0.94, and −0.91, respectively).

Suggested Citation

  • Ghorbani, Modjtaba & Alidehi-Ravandi, Razie & Amraei, Najaf & Raza, Zahid, 2024. "On the largest eigenvalue of extended eccentric matrix," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s096007792400626x
    DOI: 10.1016/j.chaos.2024.115074
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    References listed on IDEAS

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    1. Matthias Dehmer & Abbe Mowshowitz & Yongtang Shi, 2014. "Structural Differentiation of Graphs Using Hosoya-Based Indices," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-4, July.
    2. Ghorbani, Modjtaba & Li, Xueliang & Zangi, Samaneh & Amraei, Najaf, 2021. "On the eigenvalue and energy of extended adjacency matrix," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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