Research Article
BibTex RIS Cite

Skew ABC energy of digraphs

Year 2022, Volume: 71 Issue: 2, 434 - 444, 30.06.2022

N. Feyza Yalçın Şerife Büyükköse

https://doi.org/10.31801/cfsuasmas.951302
Cited By: 1

Abstract

In this paper, skew ABC matrix and its energy are introduced for digraphs. Firstly, some fundamental spectral features of the skew ABC matrix of digraphs are established. Then some upper and lower bounds are presented for the skew ABC energy of digraphs. Further extremal digraphs are determined attaining these bounds.

Keywords

ABC energy skew energy graph energy ABC matrix

References

  • Adiga, C., Balakrishnan, R., So, W., The skew energy of a digraph, Linear Algebra Appl., 432 (2010), 1825–1835. https://doi:10.1016/j.laa.2009.11.034
  • Adiga, C., Khoshbakht, Z., On some inequalities for the skew Laplacian energy of digraphs, J. Inequal. Pure and Appl. Math., 10(3) (2009), Art. 80, 6 pp.
  • Adiga, C., Smitha, M., On the skew Laplacian energy of a digraph, Int. Math. Forum, 4 (39)(2009), 1907–1914.
  • Cai, Q., Li, X., Song, J., New skew Laplacian energy of simple digraphs, Trans. Comb., 2 (2013), 27–37.
  • Chen, X., On ABC eigenvalues and ABC energy, Linear Algebra Appl., 544 (2018), 141–157. https://doi.org/10.1016/j.laa.2018.01.011
  • Estrada, E., Torres, L., Rodr´ıguez, L., Gutman, I., An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes, Indian J. Chem., 37A (1998), 849–855.
  • Estrada, E., The ABC matrix, Journal of Mathematical Chemistry, 55 (2017), 1021–1033. https://doi.org/10.1007/s10910-016-0725-5
  • Estrada, E., Atom–bond connectivity and the energetic of branched alkanes, Chem.Phys.Lett., 463 (2008), 422–425. https://doi.org/10.1016/J.CPLETT.2008.08.074
  • Furtula, B., Graovac, A., Vukiˇcevi´c, D., Atom-bond connectivity index of trees, Discrete Applied Mathematics, 157 (2008), 2828–2835. https://doi.org/10.1016/j.dam.2009.03.004
  • Furuichi, S., On refined young inequalities and reverse inequalities, J. Math. Inequal., 5 (2011), 21–31. dx.doi.org/10.7153/jmi-05-03
  • Gan, L., Hou, H., Liu, B., Some results on atom–bond connectivity index of graphs, MATCH Commun. Math. Comput. Chem., 66 (2011), 669–680.
  • Ghorbani, M., Li, X., Hakimi-Nezhaad, M., Wang, J., Bounds on the ABC spectral radius and ABC energy of graphs, Linear Algebra Appl., 598 (2020), 145–164. https://doi.org/10.1016/j.laa.2020.03.043
  • Graovac, A., Ghorbani, M., A new version of atom-bond connectivity index, Acta Chimica Slovenica, 57(3) (2010), 609–612.
  • Gu, R., Huang, X., Li, F., Skew Randi´c matrix and skew Randi´c energy, Trans. Combin., 5(1) (2016), 1–14.
  • Gutman, I., Toˇsovi´c, J. Radenkovi´c, S., Markovi´c, S., On atom-bond connectivity index and its chemical applicability, Indian J. Chem. 51A (2012), 690–694.
  • Gutman, I., The energy of a graph, Berlin Mathematics-Statistics Forschungszentrum, 103 (1978), 1–22.
  • Gutman, I., Polansky, O.E., Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
  • Kober, H., On the arithmetic and geometric means and the H¨older inequality, Proc. Amer. Math. Soc., 59 (1958), 452–459.
  • Li, X., Yang, Y., Sharp bounds for the general Randi´c index, MATCH Commun. Math. Comput. Chem., 51 (2004), 155–166.
  • Li, X., Gutman, I., Mathematical Aspects of Randi´c-type Molecular Structure Descriptors, Univ. Kragujevac, Kragujevac, 2006.
  • Li, X., Lian, H., A survey on the skew energy of oriented graphs (2015). arXiv:1304.5707v6
  • Pena, I., Rada, J., Energy of digraphs, Lin. Multilin. Algebra, 56 (2008), 565–579. https://doi.org/10.1080/03081080701482943
  • Powell, P.D., Calculating determinants of block matrices, (2011). arXiv:1112.4379
  • Randic, M., On characterization of molecular branching, J. Amer. Chem. Soc., 97 (1975), 6609–6615.
  • Shader, B., So, W., Skew spectra of oriented graphs, Elec. J. Combin., 16 (2009), 1–6.
  • Shi, L., Bounds on Randi´c indices, Discrete Math., 309(16) (2009), 5238–5241. https://doi.org/10.1016/j.disc.2009.03.036
  • Xing, R., Zhou, B., Du, Z., Further results on atom-bond connectivity index of trees, Discrete Applied Mathematics, 158 (2009), 1536–1545. https://doi.org/10.1016/j.dam.2010.05.015

Year 2022, Volume: 71 Issue: 2, 434 - 444, 30.06.2022

N. Feyza Yalçın Şerife Büyükköse

https://doi.org/10.31801/cfsuasmas.951302
Cited By: 1

Abstract

References

  • Adiga, C., Balakrishnan, R., So, W., The skew energy of a digraph, Linear Algebra Appl., 432 (2010), 1825–1835. https://doi:10.1016/j.laa.2009.11.034
  • Adiga, C., Khoshbakht, Z., On some inequalities for the skew Laplacian energy of digraphs, J. Inequal. Pure and Appl. Math., 10(3) (2009), Art. 80, 6 pp.
  • Adiga, C., Smitha, M., On the skew Laplacian energy of a digraph, Int. Math. Forum, 4 (39)(2009), 1907–1914.
  • Cai, Q., Li, X., Song, J., New skew Laplacian energy of simple digraphs, Trans. Comb., 2 (2013), 27–37.
  • Chen, X., On ABC eigenvalues and ABC energy, Linear Algebra Appl., 544 (2018), 141–157. https://doi.org/10.1016/j.laa.2018.01.011
  • Estrada, E., Torres, L., Rodr´ıguez, L., Gutman, I., An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes, Indian J. Chem., 37A (1998), 849–855.
  • Estrada, E., The ABC matrix, Journal of Mathematical Chemistry, 55 (2017), 1021–1033. https://doi.org/10.1007/s10910-016-0725-5
  • Estrada, E., Atom–bond connectivity and the energetic of branched alkanes, Chem.Phys.Lett., 463 (2008), 422–425. https://doi.org/10.1016/J.CPLETT.2008.08.074
  • Furtula, B., Graovac, A., Vukiˇcevi´c, D., Atom-bond connectivity index of trees, Discrete Applied Mathematics, 157 (2008), 2828–2835. https://doi.org/10.1016/j.dam.2009.03.004
  • Furuichi, S., On refined young inequalities and reverse inequalities, J. Math. Inequal., 5 (2011), 21–31. dx.doi.org/10.7153/jmi-05-03
  • Gan, L., Hou, H., Liu, B., Some results on atom–bond connectivity index of graphs, MATCH Commun. Math. Comput. Chem., 66 (2011), 669–680.
  • Ghorbani, M., Li, X., Hakimi-Nezhaad, M., Wang, J., Bounds on the ABC spectral radius and ABC energy of graphs, Linear Algebra Appl., 598 (2020), 145–164. https://doi.org/10.1016/j.laa.2020.03.043
  • Graovac, A., Ghorbani, M., A new version of atom-bond connectivity index, Acta Chimica Slovenica, 57(3) (2010), 609–612.
  • Gu, R., Huang, X., Li, F., Skew Randi´c matrix and skew Randi´c energy, Trans. Combin., 5(1) (2016), 1–14.
  • Gutman, I., Toˇsovi´c, J. Radenkovi´c, S., Markovi´c, S., On atom-bond connectivity index and its chemical applicability, Indian J. Chem. 51A (2012), 690–694.
  • Gutman, I., The energy of a graph, Berlin Mathematics-Statistics Forschungszentrum, 103 (1978), 1–22.
  • Gutman, I., Polansky, O.E., Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
  • Kober, H., On the arithmetic and geometric means and the H¨older inequality, Proc. Amer. Math. Soc., 59 (1958), 452–459.
  • Li, X., Yang, Y., Sharp bounds for the general Randi´c index, MATCH Commun. Math. Comput. Chem., 51 (2004), 155–166.
  • Li, X., Gutman, I., Mathematical Aspects of Randi´c-type Molecular Structure Descriptors, Univ. Kragujevac, Kragujevac, 2006.
  • Li, X., Lian, H., A survey on the skew energy of oriented graphs (2015). arXiv:1304.5707v6
  • Pena, I., Rada, J., Energy of digraphs, Lin. Multilin. Algebra, 56 (2008), 565–579. https://doi.org/10.1080/03081080701482943
  • Powell, P.D., Calculating determinants of block matrices, (2011). arXiv:1112.4379
  • Randic, M., On characterization of molecular branching, J. Amer. Chem. Soc., 97 (1975), 6609–6615.
  • Shader, B., So, W., Skew spectra of oriented graphs, Elec. J. Combin., 16 (2009), 1–6.
  • Shi, L., Bounds on Randi´c indices, Discrete Math., 309(16) (2009), 5238–5241. https://doi.org/10.1016/j.disc.2009.03.036
  • Xing, R., Zhou, B., Du, Z., Further results on atom-bond connectivity index of trees, Discrete Applied Mathematics, 158 (2009), 1536–1545. https://doi.org/10.1016/j.dam.2010.05.015
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

N. Feyza Yalçın 0000-0001-5705-8658

Şerife Büyükköse 0000-0001-7629-4277

Publication Date June 30, 2022
Submission Date June 12, 2021
Acceptance Date December 5, 2021
Published in Issue Year 2022 Volume: 71 Issue: 2

Cite

APA Yalçın, N. F., & Büyükköse, Ş. (2022). Skew ABC energy of digraphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(2), 434-444. https://doi.org/10.31801/cfsuasmas.951302
AMA Yalçın NF, Büyükköse Ş. Skew ABC energy of digraphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2022;71(2):434-444. doi:10.31801/cfsuasmas.951302
Chicago Yalçın, N. Feyza, and Şerife Büyükköse. “Skew ABC Energy of Digraphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 2 (June 2022): 434-44. https://doi.org/10.31801/cfsuasmas.951302.
EndNote Yalçın NF, Büyükköse Ş (June 1, 2022) Skew ABC energy of digraphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 2 434–444.
IEEE N. F. Yalçın and Ş. Büyükköse, “Skew ABC energy of digraphs”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 2, pp. 434–444, 2022, doi: 10.31801/cfsuasmas.951302.
ISNAD Yalçın, N. Feyza - Büyükköse, Şerife. “Skew ABC Energy of Digraphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/2 (June 2022), 434-444. https://doi.org/10.31801/cfsuasmas.951302.
JAMA Yalçın NF, Büyükköse Ş. Skew ABC energy of digraphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:434–444.
MLA Yalçın, N. Feyza and Şerife Büyükköse. “Skew ABC Energy of Digraphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 2, 2022, pp. 434-4, doi:10.31801/cfsuasmas.951302.
Vancouver Yalçın NF, Büyükköse Ş. Skew ABC energy of digraphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(2):434-4.

Cited By

ABC energies and spectral radii of some graph operations
Frontiers in Physics
https://doi.org/10.3389/fphy.2022.1053038

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.