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Articles

On α-adjacency energy of graphs and Zagreb index

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Pages 39-46 | Received 18 May 2020, Accepted 10 Apr 2021, Published online: 13 May 2021

References

  • Cvetković, D. M., Doob, M., Sachs, H. (1980). Spectra of Graphs. Theory and Application. New York: Academic Press, Inc.
  • Horn, R., Johnson, C. (1985). Matrix Analysis. New York: Cambridge University Press.
  • Li, X., Shi, Y., Gutman, I. (2012). Graph Energy. New York: Springer.
  • Pirzada, S. (2012). An Introduction to Graph Theory. Orient Black Swan, Hyderabad: Universities Press.
  • Nikiforov, V. (2017). Merging the A and Q spectral theories. Appl. Anal. Discrete Math. 11: 18–107.
  • Lin, H. Q., Xue, J., Shu, J. L. (2018). On the Aα-spectra of graphs. Linear Algebra Appl. 556: 210–219.
  • Lin, H. Q., Huang, X., Xue, J. (2018). A note on the Aα-spectral radius of graphs. Linear Algebra Appl. 557: 430–437.
  • Lin, H. Q., Liu, X. G., Xue, J. (2019). Graphs determined by their Aα-spectra. Discrete Math. 342: 441–450.
  • Liu, X. G., Liu, S. Y. (2018). On the Aα-characteristic polynomial of a graph. Linear Algebra Appl. 546: 274–288.
  • Liu, S., Das, K. C., Shu, J. (2020). On the eigenvalues of Aα-matrix of graphs. Discrete Math. 343(8): 111917.
  • Liu, S., Das, K. C., Sun, S., Shu, J. (2020). On the least eigenvalue of Aα-matrix of graphs. Linear Algebra Appl. 586: 347–376.
  • Nikiforov, V., Pasten, G., Rojo, O., Soto, R. L. (2017). On the Aα-spectra of trees. Linear Algebra Appl. 520: 286–305.
  • Pirzada, S., Rather, B. A., Shaban, R. U., Chishti, T. A. (2021). On the sum of the powers of Aα eignvalues of graphs and Aα-energy like invariant. Boletim da Sociedade Paranaense de Matematica. DOI: 10.5269/bspm.52469
  • S. Pirzada, Two upper bounds on the Aα spectral radius of a connected graph. Communication in Combinatorics and Optimization. DOI: 10.22049/CCO.2021.27061.1187
  • Xue, J., Lin, H., Liu, S. T, Shu, J. L. (2018). On the Aα-spectral radius of a graph. Linear Algebra Appl 550: 105–120.
  • Gutman, I. (1978). The energy of a graph. Ber. Math. Statist. Sekt. Forschungsz. Graz. 103: 1–22.
  • Gutman, I., Zhou, B. (2006). Laplacian energy of a graph. Linear Algebra Appl. 414(1): 29–37.
  • Gutman, I. (2001). The energy of a graph: Old and new results. In: Betten, A., Kohnert, A., Laue, R., Wassermann, A., eds. Algebraic Combinatorics and Applications. Berlin: Springer-Verlag, pp. 196–211.
  • Abreu, N., Cardoso, D. M., Gutman, I., Martins, E. A., Robbiano, M. A. (2011). Bounds for the signless Laplacian energy. Linear Algebra Appl. 435(10): 2365–2374.
  • Arizmendi, G., Arizmendi, O. (2021). Energy of a graph and Randic index. Linear Algebra Appl. 609: 332–338.
  • Das, K. C., Alazemi, A., Anđelić, M. (2020). On energy and Laplacian energy of chain graphs. Discrete Appl. Math. 284: 391–400.
  • Ganie, H. A., Chat, B. A., Pirzada, S. (2018). On the signless Laplacian energy of a graph and energy of line graph. Linear Algebra Appl. 544: 306–324.
  • Pirzada, S., Ganie, H. A. (2015). On the Laplacian eigenvalues of a graph and Laplacian energy. Linear Algebra Appl. 486: 454–468.
  • Gou, H., Zhou, B. (2018). On the α spectral radius of graphs, arXiv:1805.03245v1.
  • Koolen, J. H., Moulton, V. (2001). Maximal energy graphs. Adv. Appl. Math. 26(1): 47–52.