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A note on the minimum edge dominating energy of graphs

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Abstract

Let G be a graph with n vertices and m edges. The edges energy is defined as the sum of the absolute values of eigenvalues of the adjacency matrix of line graph of G. In this paper, the minimum edge dominating energy of the graph G is introduced and the minimum edge dominating energy of some graphs is computed. We also investigate the bounds of the minimum edge dominating energy of graphs.

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References

  1. Gutman, I.: The energy of a graph. Ber. Math-Stat. Sekt. Forschungsz. Graz. 103, 1–22 (1978)

    MATH  Google Scholar 

  2. Liu, H., Lu, M., Tian, F.: Some upper bounds for the energy of graphs. J. Math. Chem. 41, 45–57 (2007)

    Article  MathSciNet  Google Scholar 

  3. Ma, X.: A low bound on graph energy in terms of minimum degree. MATCH Commun. Math. Comput. Chem. 81(2), 393–404 (2019)

    Google Scholar 

  4. Ashraf, F.: On energy of trees with perfect matching. MATCH Commun. Math. Comput. Chem. 82(2), 439–442 (2019)

    Google Scholar 

  5. Jahanbani, A.: Upper bounds for the energy of graphs. MATCH Commun. Math. Comput. Chem. 79(2), 275–286 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Alawiah, N., Rad, N.J., Jahanbani, A., Kamarulhaili, H.: New upper bounds on the energy of a graph. MATCH Commun. Math. Comput. Chem. 79(2), 287–301 (2018)

    MathSciNet  Google Scholar 

  7. Graovac, A., Gutman, I., Trinajstic, N.: Topological Approach to the Chemistry of Conjugated Molecules. Springer, Berlin (1977)

    Book  Google Scholar 

  8. Gutman, I., Polansky, O.E.: Mathematical Concepts in Organic Chemistry. Springer, Berlin (1986)

    Book  Google Scholar 

  9. Cvetkovic, D., Gutman, I.: Applications of Graph Spectra. Mathematical Institution, Belgrade (2009)

    MATH  Google Scholar 

  10. Cvetkovic, D., Gutman, I.: Selected Topics on Applications of Graph Spectra. Zbornik radova 14 (22). Mathematical Institute SANU, Belgrade (2011)

    MATH  Google Scholar 

  11. Allem, L.E., Molina, G., Pastine, A.: Short note on Randic energy. MATCH Commun. Math. Comput. Chem. 82(2), 515–528 (2019)

    Google Scholar 

  12. Li, H.H., Hou, Y.X., Su, L.: Graphs with extremal matching energies and prescribed parameters. MATCH Commun. Math. Comput. Chem. 72, 239–248 (2014)

    MathSciNet  MATH  Google Scholar 

  13. Bozkurt, S.B., Bozkurt, D.: On incidence energy. MATCH Commun. Math. Comput. Chem. 72, 215–225 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Das, C., Gutman, I.: Comparing Laplacian energy and Kirchhoff index. MATCH Commun. Math. Comput. Chem. 81(2), 419–424 (2019)

    Google Scholar 

  15. Zhu, J.: On minimal energies of unicyclic graphs with perfect matching. MATCH Commun. Math. Comput. Chem. 70, 97–118 (2013)

    MathSciNet  MATH  Google Scholar 

  16. Das, K.C.: Conjectures on resolvent energy of graphs. MATCH Commun. Math. Comput. Chem. 81(2), 453–464 (2019)

    Google Scholar 

  17. Akbari, S., Ghodrati, A.H., Gutman, I., Hosseinzadeh, M.H., Konstantinova, E.V.: On path energy of graphs. MATCH Commun. Math. Comput. Chem. 81(2), 465–470 (2019)

    MathSciNet  Google Scholar 

  18. Das, K.C.: On the Zagreb energy and Zagreb Estrada index of graphs. MATCH Commun. Math. Comput. Chem. 82(2), 529–542 (2019)

    MathSciNet  Google Scholar 

  19. Dilek Maden, A.: New bounds on the normalized Laplacian (Randic) energy. MATCH Commun. Math. Comput. Chem. 79(2), 321–330 (2018)

    MathSciNet  Google Scholar 

  20. Liu, X., Wang, L., Xiao, P.: Ordering of bicyclic graphs by matching energy. MATCH Commun. Math. Comput. Chem. 79(2), 341–365 (2018)

    MathSciNet  Google Scholar 

  21. Palacios, J.L.: Lower bounds for the Laplacian resolvent energy via majorization. MATCH Commun. Math. Comput. Chem. 79(2), 367–370 (2018)

    MathSciNet  Google Scholar 

  22. Kaya, E., Maden, A.D.: A generalization of the incidence energy and the Laplacian-energy-like invariant. MATCH Commun. Math. Comput. Chem. 80(2), 467–480 (2018)

    MathSciNet  Google Scholar 

  23. Rajesh Kanna, M.R., Dharmendra, B.N., Sridhara, G.: The minimum dominating energy of a graph. Int. J. Pure Appl. Math. 85, 707–718 (2013)

    MATH  Google Scholar 

  24. Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)

    Book  Google Scholar 

  25. Alikhani, S., Mohebbi, F.: On the edge energy of some specific graphs. J. Math. Nanosci. 7(1), 15–21 (2017)

    Google Scholar 

  26. Milovanović, I.Z., Milovanović, E.I.: Remarks on the energy and the minimum dominating energy of a graph. MATCH. Commun. Math. Comput. Chem. 75, 305–314 (2016)

    MathSciNet  MATH  Google Scholar 

  27. Gutman, I., Robbiano, M., Martins, E.A., Cardoso, D.M., Medina, L., Rojo, O.: Energy of line graphs. Linear Algebra Appl. 433, 1312–1323 (2010)

    Article  MathSciNet  Google Scholar 

  28. Ramane, H.S., Walikar, H.B., Rao, S.B., Acharya, B.D., Hampiholi, P.R.: Spectra and energies of iterated line graphs of regular graphs. Appl. Math. Lett. 18, 679–682 (2005)

    Article  MathSciNet  Google Scholar 

  29. Gupta, R.P.: Independence and covering numbers of line graphs and total graphs. In: Harary, F. (ed.) Proof Techniques in Graph Theory, pp. 61–62. Academic press, New York (1969)

    Google Scholar 

  30. Gutman, I., Trinajstić, N.: Graph theory and molecular orbitals. Total \(\pi \)-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972)

    Article  Google Scholar 

  31. Aldaz, J.M., Barza, S., Fujii, M., Moslehian, M.S.: Advances in operator Cauchy–Schwarz inequalities and their reverses. Ann. Funct. Anal. 6(3), 275–295 (2015)

    Article  MathSciNet  Google Scholar 

  32. Bapat, R.B.: Graphs and Matrices. Hindustan Book Agency, New Delhi (2011)

    MATH  Google Scholar 

  33. Koolen, J.H., Moulton, V.: Maximal energy graphs. Adv. Appl. Math. 26, 47–52 (2001)

    Article  MathSciNet  Google Scholar 

  34. Polya, G., Szego, G.: Problems and Theorems in Analysis. Series. Integral Calculus. Theory of Functions. Springer, Berlin (1972)

    Book  Google Scholar 

  35. Ozeki, N.: On the estimation of inequalities by maximum and minimum values. J. Coll. Arts Sci. Chiba Univ. 5, 199–203 (1968)

    MathSciNet  Google Scholar 

  36. Mitrinović, D.S., Vasić, P.M.: Analytic Inequalities. Springer, Berlin (1970)

    Book  Google Scholar 

  37. Niculescu, C., Persson, L.E.: Convex Functions and Their Applications: A Contemporary Approach. Springer, New York (2006)

    Book  Google Scholar 

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Acknowledgements

The authors would like to thank Professor Ivan Gutman for his useful comments and suggestions.

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Authors and Affiliations

  1. School of Civil Engineering, Universiti Sains Malaysia, Nibong Tebal, Penang, Malaysia

    Mohammad Hadi Akhbari & Kok Keong Choong

  2. Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

    Fateme Movahedi

Authors
  1. Mohammad Hadi Akhbari
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  2. Kok Keong Choong
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  3. Fateme Movahedi
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Correspondence to Kok Keong Choong.

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Akhbari, M.H., Choong, K.K. & Movahedi, F. A note on the minimum edge dominating energy of graphs. J. Appl. Math. Comput. 63, 295–310 (2020). https://doi.org/10.1007/s12190-020-01318-7

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  • DOI: https://doi.org/10.1007/s12190-020-01318-7

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