Abstract
Introduction/purpose: In the current literature, several dozens of vertexdegree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated. The VDB energy is the energy (= sum of the absolute values of the eigenvalues) of the respective VDB matrix. The paper examines some general properties of the VDB energy of bipartite graphs.
Results: Estimates (lower and upper bounds) are established for the VDB energy of bipartite graphs in which there are no cycles of size divisible by 4, in terms of ordinary graph energy.
Conclusion: The results of the paper contribute to the spectral theory of VDB matrices, especially to the general theory of VDB energy.
Keywords
Array
Array
Array
References
Cvetković, D., Rowlinson, P. & Simić, K. 2010. An Introduction to the Theory of Graph Spectra. Cambridge: Cambridge University Press. ISBN: 9780521134088.
Das, K.C., Gutman, I., Milovanović, I., Milovanović, E. & Furtula, B. 2018. Degree-based energies of graphs. Linear Algebra and its Applications, 554, pp.185-204. Available at: https://doi.org/10.1016/j.laa.2018.05.027
Gutman, I. 1977. Acyclic systems with extremal Hückel π-electron energy. Theoretica chimica acta, 45, pp.79-87. Available at: https://doi.org/10.1007/BF00552542
Gutman, I. 2020. Relating graph energy with vertex-degree-based energies. Vojnotehnički glasnik/Military Technical Courier, 68(4), pp.715-725. Available at: https://doi.org/10.5937/vojtehg68-28083
Gutman, I. 2021. Comparing degree-based energies of trees. Contributions to Mathematics, 4, pp.1-5. Available at: https://doi.org/10.47443/cm.2021.0030
Gutman, I. & Cyvin, S.J. 1989. Introduction to the theory of benzenoid hydrocarbons. Berlin: Springer. Available at: https://doi.org/10.5860/choice.27-4521
Gutman, I., Monsalve, J. & Rada, J. 2022. A relation between a vertexdegree-based topological index and its energy. Linear Algebra and its Applications, 636(March), pp.134-142. Available at: https://doi.org/10.1016/j.laa.2021.11.021
Gutman, I., Redžepović, I. & Rada, J. 2021. Relating energy and Sombor energy. Contributions to Mathematics, 4, pp.41-44. Available at: https://doi.org/10.47443/cm.2021.0054
Kulli, V.R. 2020. Graph indices. In: Pal, M., Samanta, S. & Pal, A. (Eds.), Handbook of Research of Advanced Applications of Graph Theory in Modern Society, pp.66-91. Hershey, USA: IGI Global. Available at:
https://doi.org/10.4018/978-1-5225-9380-5.ch003
Li, X., Shi, Y. & Gutman, I. 2012. Introduction. In: Graph Energy, pp.1-9. New York, NY: Springer. Available at: https://doi.org/10.1007/978-1-4614-4220-2_1
Li, X. & Wang, Z. 2021. Trees with extremal spectral radius of weighted adjacency matrices among trees weighted by degree-based indices. Linear Algebra and Its Applications, 620, pp.61-75. Available at:
https://doi.org/10.1016/j.laa.2021.02.023
Ramane, H.S. 2020. Energy of graphs. In: Pal, M., Samanta, S., & Pal, A. (Eds.) Handbook of Research on Advanced Applications of Graph Theory in Modern Society, pp.267-296. Hershey, PA, USA: IGI Global. Available at:
https://doi.org/10.4018/978-1-5225-9380-5.ch011
Shao, Y., Gao, Y., Gao, W. & Zhao, X. 2021. Degree-based energies of trees. Linear Algebra and Its Applications, 621, pp.18-28. Available at: https://doi.org/10.1016/j.laa.2021.03.009
Todeschini, R. & Consonni, V. 2009. Molecular Descriptors for Chemoinformatics. Weinheim: Wiley-VCH. ISBN: 978-3-527-31852-0.
Proposed Creative Commons Copyright Notices
Proposed Policy for Military Technical Courier (Journals That Offer Open Access)
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).