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Year 2020, , 238 - 247, 01.03.2020

İlkay Altındağ

https://doi.org/10.35378/gujs.532697
Cited By: 1

Abstract

References

  • 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).

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

Year 2020, , 238 - 247, 01.03.2020

İlkay Altındağ

https://doi.org/10.35378/gujs.532697
Cited By: 1

Abstract

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

References

  • 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).
There are 29 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

İlkay Altındağ 0000-0001-5359-8964

Publication Date March 1, 2020
Published in Issue Year 2020

Cite

APA Altındağ, İ. (2020). Generalization for the Average Value of the Difference Between the Energies of Two Graphs. Gazi University Journal of Science, 33(1), 238-247. https://doi.org/10.35378/gujs.532697
AMA Altındağ İ. Generalization for the Average Value of the Difference Between the Energies of Two Graphs. Gazi University Journal of Science. March 2020;33(1):238-247. doi:10.35378/gujs.532697
Chicago Altındağ, İlkay. “Generalization for the Average Value of the Difference Between the Energies of Two Graphs”. Gazi University Journal of Science 33, no. 1 (March 2020): 238-47. https://doi.org/10.35378/gujs.532697.
EndNote Altındağ İ (March 1, 2020) Generalization for the Average Value of the Difference Between the Energies of Two Graphs. Gazi University Journal of Science 33 1 238–247.
IEEE İ. Altındağ, “Generalization for the Average Value of the Difference Between the Energies of Two Graphs”, Gazi University Journal of Science, vol. 33, no. 1, pp. 238–247, 2020, doi: 10.35378/gujs.532697.
ISNAD Altındağ, İlkay. “Generalization for the Average Value of the Difference Between the Energies of Two Graphs”. Gazi University Journal of Science 33/1 (March 2020), 238-247. https://doi.org/10.35378/gujs.532697.
JAMA Altındağ İ. Generalization for the Average Value of the Difference Between the Energies of Two Graphs. Gazi University Journal of Science. 2020;33:238–247.
MLA Altındağ, İlkay. “Generalization for the Average Value of the Difference Between the Energies of Two Graphs”. Gazi University Journal of Science, vol. 33, no. 1, 2020, pp. 238-47, doi:10.35378/gujs.532697.
Vancouver Altındağ İ. Generalization for the Average Value of the Difference Between the Energies of Two Graphs. Gazi University Journal of Science. 2020;33(1):238-47.

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