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Complementary distance Seidel equienergetic graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 11، شماره 2، شهریور 2026، صفحه 99-106 اصل مقاله (326.88 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.12527.1165 | ||
| نویسندگان | ||
| Indulal G Gopalapillai* 1؛ Deena Scaria1؛ Jinu Mary2 | ||
| 1Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, Kerala, India | ||
| 2Department of Mathematics, Mar Thoma College, Tiruvalla, Pathanamthitta-689103, India | ||
| تاریخ دریافت: 27 شهریور 1404، تاریخ بازنگری: 22 آبان 1404، تاریخ پذیرش: 16 آذر 1404 | ||
| چکیده | ||
| The distance matrix, its eigenvalues, and the corresponding distance energy of a connected graph have been extensively studied in the literature. However, research on the Distance Seidel matrix associated with a connected graph remains in its developmental stages. The Distance Seidel matrix of a graph yields the Distance Seidel eigenvalues ∂1S ≥ ∂2S ≥ … , ∂nS, which together constitute the Distance Seidel spectrum of G. In [1], the authors introduced the complementary distance matrix and studied its properties. Motivated by these we introduce the complementary distance seidel matrix of a connected graph and obtain some results for some classes of graphs. In this paper, we investigate the Complementary Distance Seidel Spectrum of complement of line graphs of regular graphs. | ||
| کلیدواژه‌ها | ||
| complementary distance Seidel matrix؛ complementary distance Seidel spectrum؛ complementary distance Seidel equienergetic graphs | ||
| مراجع | ||
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[1] F. Buckley, Iterated line graphs, Congr. Numer. 33 (1981) 390–394. [2] F. Buckley, The set of iterated line graphs, Graph Theory Notes of New York 25 (1993) 33–36. [3] D. M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs: Theory and Application, Academic Press, New York, 1980. [4] D. M. Cvetković, P. Rowlinson, S. K. Simić, An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge, 2010. https://doi.org/10.1017/CBO9780511801518 [5] T. Haritha, A. V. Chithra, Distance Seidel matrix of a connected graph, arXiv:2210.05940 (2022). https://arxiv.org/abs/2210.05940 [6] G. Indulal, I. Gutman, A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008) 461–472. https://match.pmf.kg.ac.rs/ electronic_versions/ Match60/n2/ match60n2_461-472.pdf [7] G. Indulal, D-spectrum and D-energy of complements of iterated line graphs of regular graphs, J. Algebraic Struct. Appl. 4 (2017) 51–56. https://doi.org/10.29252/asta.4.1.51 [8] G. Indulal, D. C. Scaria, The distance-related spectra of some subdivision-related graphs, J. Comput. Sci. Appl. Math. 3 (2021) 23–36. https://doi.org/10.37418/jcsam.3.1.4 [9] O. Ivanciuc, T. Ivanciuc, A. T. Balaban, The complementary distance matrix, a new molecular graph metric, ACH Models Chem. 137 (2000) 57–82. [10] D. Jenezić, A. Milićević, S. Nikolić, N. Trinajstić, Graph Theoretical Matrices in Chemistry, Univ. Kragujevac, Kragujevac, 2007. https://doi.org/10.1201/b18389 [11] H. S. Ramane, K. C. Nandeesh, Complementary distance spectra and complementary distance energy of line graphs of regular graphs, J. Indones. Math. Soc. 22 (2016) 27–35. https://doi.org/10.22342/jims.22.1.205.27-35 | ||
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