Average Degree-Eccentricity Energy of Graphs

Document Type: Original Scientific Paper

Authors

1 University Kragujevac, Serbia

2 Department of Mathematics University of Mysore Mysuru, India

3 Department of Studies in Mathematics, Faculty of Science and Technology Manasagangotri, University of Mysore, Mysore, India.

Abstract

The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.

Keywords

Main Subjects


1. C. Adiga, M. Smitha, On maximum degree energy of a graph, Int. J. Contemp. Math. Sci. 4 (2009) 385–396.

2. R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004) 287–295.

3. H. E. Bell, Gerschgorin’s theorem and the zeros of polynomials, Am. Math. Monthly 72 (1965) 292–295.

4. D. J. H. Garling, Inequalities – A Journey Into Linear Analysis, Cambridge Univ. Press, Cambridge, 2007.

5. I. Gutman, The energy of a graph, Ber. Math.–Statist. Sekt. Forsch. Graz 103 (1978) 1–22.

6. I. Gutman, B. Furtula, Survey of graph energies, Math. Interdisc. Res. 2 (2017) 85–129.

7. I. Gutman, B. Furtula, The total Pi-electron energy saga, Croat. Chem. Acta 90 (2017) 359–368.

8. F. Harary, Graph Theory, Addison Wesley, Reading, 1969.

9. N. Jafari Rad, A. Jahanbani, I. Gutman, Zagreb energy and Zagreb Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 79 (2018) 371–386.

10. X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.

11. V. Mathad, S. S. Mahde, The minimum hub energy of a graph, Palest. J. Math. 6 (2017) 247–256.

12. B. J. McClelland, Properties of the latent roots of a matrix: The estimation of pi-electron energies, J. Chem. Phys. 54 (1971) 640–643.

13. M. A. Naji, N. D. Soner, The maximum eccentricity energy of a graph, Int. J. Sci. Engin. Res. 7 (2016) 5–13.

14. H. S. Ramane, I. Gutman, J. B. Patil, R. B. Jummannaver, Seidel signless Laplacian energy of graphs, Math. Interdisc. Res. 2 (2017) 181–192.

15. D. S. Revankar, M. M. Patil, H. S. Ramane, On eccentricity sum eigenvalue and eccentricity sum energy of a graph, Ann. Pure Appl. Math. 13 (2017) 125–130.

16. B. Sharada, M. I. Sowaity, I. Gutman, Laplacian sum-eccentricity energy of a graph, Math. Interdisc. Res. 2 (2017) 209–219.

17. M. I. Sowaity, B. Sharada, The sum-eccentricity energy of a graph, Int. J. Rec. Innovat. Trends Comput. Commun. 5 (2017) 293–304.