Energy and Randić energy of special graphs

• T. K., Jahfar ^[1] ; A. V., Chithra ^[1]
  1. [1] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 4, 2022, págs. 855-877
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4616
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph invariants like the degree Kirchhoff index, the Kemeny’s constant and the number of spanning trees of some special graphs. From our results, we indicate how to obtain infinitely many pairs of equienergetic graphs, Randić equienergetic graphs and also, infinite families of integral graphs.

• Referencias bibliográficas
  • S. Alikhani and N. Ghanbari, “Randić energy of specific graphs”, Applied Mathematics and Computation, vol. 269, pp. 722-730, 2015. https://doi.org/10.1016/j.amc.2015.07.112
  • I. Altindag, “Some statistical results on Randić energy of graphs”, Match (Mülheim), vol. 79, pp. 331-339, 2018. [On line]. Available: https://bit.ly/3PB0Xwr
  • R. Balakrishnan, “The energy of a graph”, Linear Algebra and its Applications, vol. 387, pp. 287-295, 2004. https://doi.org/10.1016/j.laa.2004.02.038
  • S. Burcu Bozkurt, A Dilek Gungor, I. Guntman, and A. Sinan Cevik, “Randić matrix and Randić energy”, Match (Mülheim), vol. 64, no. 1, pp....
  • S. Butler, “Algebraic aspects of the normalized Laplacian,” in Recent Trends in Combinatorics, A. Beveridge, J. Griggs, L. Hogben, G. Musiker,...
  • H. Chen and F. Zhang, “Resistance distance and the normalized Laplacian spectrum”, Discrete Applied Mathematics, vol. 155, no. 5, pp. 654-661,...
  • Z.-Q. Chu, S. Nazeer, T. J. Zia, I. Ahmed, and S. Shahid, “Some new results on various graph energies of the splitting graph”, Journal of...
  • F. R. K. Chung, Spectral graph theory, vol. 92. Providence, RI: American Mathematical Society, 1997. https://doi.org/10.1090/cbms/092
  • D. M. Cvetković, M. Doob and H. Sachs, Spectral of graphs: Theory and applications, vol. 10. New York, NY: Academic Press, 1980.
  • K. C. Das, S. Sun and I. Gutman, “Normalized Laplacian eigenvalues and Randić energy of graphs”, Match (Mülheim), vol. 77, no. 1, pp. 45-59,...
  • I. Gutman, “The energy of a graph”, Berichte der Mathematisch-Statistischen Sektion in der Forschungsgesellschaft Joanneum, no. 103, pp. 100-105,...
  • I. Gutman, B. Furtula and S. Burcu Bozkurt, “On Randić energy”, Linear Algebra and its Applications, vol. 442, pp. 50-57, 2014. https://doi.org/10.1016/j.laa.2013.06.010
  • J. J. Hunter, “The role of Kemeny’s constant in properties of Markov chains”, Communications in Statistics- Theory and Methods, vol. 43, no....
  • G. Indulal and A. Vijayakumar, “On a pair of equienergetic graphs”, Match (Mülheim), vol. 55, no. 1, pp. 83-90, 2006. [On line]. Available:...
  • D. J. Klein and M. Randić, “Resistance distance”, Journal of mathematical chemistry, vol. 12, no. 1, pp. 81-95, 1993. https://doi.org/10.1007/BF01164627
  • E. Munarini, C. Perelli Cippo, A. Scagliola and N. Zagaglia Salvi, “Double graphs”, Discrete mathematics, vol. 38, no. 2-3, pp. 242-254, 2008....
  • H. P. Patil and V. Raja, “On tensor product of graphs, girth and triangles”, Iranian Journal of Mathematical Sciences and Informatics, vol....
  • H. S. Ramane, H. B. Walikar, S. Bhaskara Rao, B. D. Acharya, P. R Hampiholi. S. R. Jog, and I. Gutman, “Equienergetic graphs”, Kragujevac...
  • O. Rojo and L. Medina, “Construction of bipartite graphs having the same Randić energy”, Match (Mülheim), vol. 68, no. 3, pp. 805-814, 2012....
  • E. Sampathkumar, “On duplicate graphs”, Journal of the Indian Mathematical Society, vol. 37, pp. 285-293, 1973. [On line]. Available: https://bit.ly/3PPrjKP
  • E. Sampathkumar and H. B. Walikar, “On splitting graph of a graph”, Karnatak University journal of science, vol. 25, no. 13, pp. 13-16, 1981....
  • S. K. Vaidya and K. M. Popat, “Energy of m-splitting and m-shadow graphs”, Far East Journal of Mathematical Sciences, vol. 102, pp. 1571-1578,...