İlkay ALTINDAĞ

Generalization for the Average Value of the Difference Between the Energies of Two Graphs

Let G denote the set of all simple graphs with n vertices and m edges. In this paper, for a given type of graph Hermite matrix A, we determine the average values of the difference between A-energies of two graphs randomly chosen from G . These results yield criterions for deciding when two graphs are almost A-equienergetic. Our results generalize some previous results in the literature. Moreover, we give new results on Laplacian energy.

Keywords:

(A-) energy of graph almost (A-) equienergetic graphs,

PDF

___

Altindag, I., "Some statistical results for Randi´c energy of graphs", MATCH Commun. Math. Comput. Chem., 79: 331-339, (2018).
Andriantiana, E.O.D., "Laplacian energy", In: Gutman, I., Li, X. ed., Energies of Graphs -Theory and Applications, Univ. Kragujevac, Kragujevac,49-80, (2016).
Balakrishnan, R., "The energy of a graph", Lin. Algebra Appl., 387: 287-295, (2004).
Bozkurt, S.B., Gungor, A.D., Gutman, I., Cevik, A.S., "Randi´c matrix and Randi´c energy", MATCH Commun. Math. Comput. Chem., 64: 239-250, (2010).
Brankov, V., Stevanovi´c, D., Gutman, I., "Equienergetic chemical trees", J. Serb. Chem. Soc., 69: 549-553, (2004).
Cvetkovi´c, D., Doob, M., Sachs, H., Spectra of Graphs-Theory and Application, Academic Press, New York, (1980).
Ganie, H., Pirzada, L., Iványi, A., "Energy, Laplacian energy of double graphs and new families of equienergetic graphs", Acta Univ. Sapientiae Informatica, 6: 89-116, (2014).
Graovac, A., Gutman, I., John, P.E., Vidovi´c, D., Vlah, I., "On statistics of graph energy", Z. Naturforsch., 56a: 307-311, (2001).
Gutman, I., "The energy of a graph", Ber. Math. Stat. Sekt. Forschungsz. Graz, 103: 1-22, (1978).
Gutman, I., "Total pi-electron energy of benzenoid hydrocarbons", Topics Curr. Chem., 162: 29-63, (1992).
Gutman, I., "The energy of a graph: old and new results", In: Betten, A., Kohnert, A., Laue, R., Wassermann A. ed., Algebraic Combinatorics andApplications, Springer-Verlag, Berlin, 196-211, (2001).
Gutman, I., "Topology and stability of conjugated hidrocarbons. The dependence of total pi-electron energy on molecular topology", J. Serb. Chem.Soc. 70: 441-456, (2005).
Gutman, I., "Comparative studies of graph energies", Bulletin del'Acad´emie Serbe des Sciences et des Arts (Classe des SciencesMath´ematiques et Naturelles), 144: 1-17, (2012).
Gutman, I., Li, X., Zhang, J., "Graph energy", In: Dehmer, M., Emmert-Streib F. ed., Analysis of Complex Networks From Biology to Linguistics,Wiley-VCH, Weinheim, 145-174, (2009).
Gutman, I., Zhou, B., "Laplacian energy of a graph", Lin. Algebra Appl., 414: 29-37, (2006).
Horn, R.A., Johnson, C.R., Matrix Analysis, Cambridge Univ. Press, Cambridge, (1985).
Indulal, G., Vijayakumar, A., "On a pair of equienergetic graphs", MATCH Commun. Math. Comput. Chem., 55: 83-90, (2006).
Li, X., Shi, Y., Gutman, I., Graph Energy, Springer, New York, (2012).
Liu, J., Liu, B., "Generalization for Laplacian energy", Appl. Math. J. Chinese Univ., 24: 443-450, (2009).
Liu, J., Liu, B., Radenkovi´c, S., Gutman, I., "Minimal LEL-equienergetic graphs", MATCH Commun. Math. Comput. Chem., 61: 471-478, (2009).
Merris, R., "A survey of graph Laplacians", Lin. Multilin. Algebra, 39: 19-31, (1995).
Miljkovi´c, O., Furtula, B., Radenkovi´c, S., Gutman, I., "Equienergetic and almost-equienergetic trees", MATCH Commun. Math. Comput. Chem.,61: 451-461, (2009).
Pirzada S., Ganie, H.A., "On the construction of L-equienergetic graphs", AKCE International J. Graphs Combin., 12: 141-154, (2015).
Ramane, H.S., Walikar, H.B., "Construction of equienergetic graphs", MATCH Commun. Math. Comput. Chem., 57: 203-210, (2007).
Stani´c, M.P., Gutman, I., "On almost-equienergetic graphs", MATCH Commun. Math. Comput. Chem., 70: 681-688, (2013).
Stani´c, M.P., Gutman, I., "Towards a definition of almost-equienergetic graphs", J. Math. Chem., 52: 213-221, (2014).
Stevanovi´c, D., "Large sets of noncospectral graphs with equal Laplacian energy", MATCH Commun. Math. Comput. Chem., 61: 463-470, (2009).
Zhou, B., Gutman, I., "On Laplacian energy of graphs", MATCH Commun. Math. Comput. Chem., 57: 211-220, (2007).
Zumstein, P., "Comparison of spectral methods through the adjacency matrix and the Laplacian of a graph", Diploma Thesis, ETH Zurich, (2005).