Skew ABC energy of digraphs
Year 2022,
Volume: 71 Issue: 2, 434 - 444, 30.06.2022
N. Feyza Yalçın
,
Şerife Büyükköse
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.
References
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Year 2022,
Volume: 71 Issue: 2, 434 - 444, 30.06.2022
N. Feyza Yalçın
,
Şerife Büyükköse
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