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Analyzing Energy and Defining New Classes of Borderenergetic Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 اردیبهشت 1405 اصل مقاله (474.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30915.2666 | ||
| نویسندگان | ||
| Yasir Bashir1؛ Bilal A. Chat* 1؛ Hilal A. Ganie2 | ||
| 1Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India | ||
| 2Department of Mathematics, Govt. Degree College Uri, JK Government, India | ||
| چکیده | ||
| In graph theory, the \textit{energy} of a graph \( G \), denoted as \( \mathcal{E}(G) \), is quantified by \(\mathcal{E}(G) = \sum_{i=1}^{n} |\lambda_i|\), where the eigenvalues \( \lambda_1, \lambda_2, \ldots, \lambda_n \) derive from the adjacency matrix of \( G \), and \( n \) represents the vertex total. This research investigates the conditions enabling line graphs of non-regular structures to transform into borderenergetic forms, emphasizing structural traits that drive this transition. The focus includes irregular graphs like the complete bipartite graphs \(K_{a,b}\) across varying \( a \) and \( b \). We also examine corona products, exemplified by \( K_{a,b} \circ K_r \), to identify conditions for the emergence of borderenergetic graphs, thus enhancing comprehension of these graphs through structural and spectral perspectives. | ||
| کلیدواژهها | ||
| graphs؛ rank؛ eigenvalues؛ energy؛ topological index | ||
| مراجع | ||
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[1] K. Balinska, D. Cvetković, M. Lepović, and S. Simić, There are exactly 150 connected integral graphs up to 10 vertices, Publ. Elektrotehn. Fak. (Beograd), Ser. Mat. 10 (1999), 95–105.
[2] S. Cui and G. Tian, The spectrum and the signless Laplacian spectrum of coronae, Linear Algebra Appl. 437 (2012), no. 7, 1692–1703. https://doi.org/10.1016/j.laa.2012.05.019
[3] D. Cvetkovic, M. Doob, and H. Sachs, Spectra of Graphs-Theory and Application, Academic Press, New York, 1980.
[4] D. Cvetković, I. Gutman, and N. Trinajstić, Conjugated molecules having integral graph spectra, Chem. Phys. Lett. 29 (1974), no. 1, 65–68. https://doi.org/10.1016/0009-2614(74)80135-1
[5] D. Cvetković, P. Rowlinson, and S. Simić, An Introduction to the Theory of Graph Spectra, Cambridge University Press, Cambridge, 2009.
[6] C. Dede and A.D. Maden, Almost borderenergetic line graphs, Discrete Math. Algorithms Appl. 17 (2024), no. 4, 2450062. https://doi.org/10.1142/S1793830924500629
[7] S. Gong, X. Li, G. Xu, I. Gutman, and B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 74 (2015), no. 2, 321–332.
[8] I. Gutman and K.C. Das, Estimating the total-electron energy, J. Serb. Chem. Soc. 78 (2013), 1925–1933. https://doi.org/10.2298/JSC130905092G
[9] I. Gutman, M. Robbiano, E.A. Martins, D.M. Cardoso, L. Medina, and O. Rojo, Energy of line graphs, Linear Algebra Appl. 433 (2010), no. 7, 1312–1323. https://doi.org/10.1016/j.laa.2010.05.009
[10] W.H. Haemers, Strongly regular graphs with maximal energy, Linear Algebra Appl. 429 (2008), no. 11-12, 2719–2723. https://doi.org/10.1016/j.laa.2008.03.024 [11] T.K. Jahfar, V.K. Najiya, and A.V. Chithra, Construction of new families of borderenergetic graphs, AIP Conference Proceedings 2336 (2021), no. 1, 050002.
[12] Q. Li and L. Tang, Infinite numbers of infinite classes L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 90 (2023), no. 3, 729–742. https://doi.org/10.46793/match.90-3.729L
[13] X. Li, M. Wei, and X. Zhu, Borderenergetic graphs with small maximum or large minimum degrees, MATCH Commun. Math. Comput. Chem. 77 (2017), 25–36.
[14] X. Lv, B. Deng, and X. Li, On the borderenergeticity of line graphs, MATCH Commun. Math. Comput. Chem. 87 (2021), no. 3, 693–702. https://doi.org/10.46793/match.87-3.693L
[15] M. Perić, I. Gutman, and J. Radić-Perić, The Hückel total π-electron energy puzzle, J. Serb. Chem. Soc. 71 (2006), no. 7, 771–783.
[16] Q. Tao and Y. Hou, q-borderenergetic graphs, AKCE Int. J. Graphs Comb. 17 (2020), no. 1, 38–44. https://doi.org/10.1016/j.akcej.2018.03.001
[17] S.K. Vaidya and K.M. Popat, Some borderenergetic and equienergetic graphs, Kragujevac J. Math. 48 (2024), no. 6, 935–949. https://doi.org/10.46793/KgJMat2406.935V | ||
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