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The distance seidel spectrum of some graph operations | ||
| Journal of Hyperstructures | ||
| دوره 13، شماره 1، 2024، صفحه 15-32 اصل مقاله (360.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2024.14425.1004 | ||
| نویسندگان | ||
| Deena Scaria؛ Indulal Gopal* | ||
| Department of Mathematics, St Aloysius College, Edathua, 689573, India | ||
| چکیده | ||
| The distance matrix, distance eigenvalue, and distance energy of a connected graph have been studied in detail in literature where as the study on distance seidel matrix associated with a connected graph is in progress. The eigenvalues ∂1S≥∂2S≥ ... ≥∂nS of the distance seidel matrix DS(G) of a graph G forms the distance seidel spectrum of G. We describe here the distance seidel spectrum of some types of subdivision related graphs of a regular graph in terms of its adjacency spectrum. We also derive analytic expressions for the distance seidel energy of G(Cp), the partial complement of the subdivision graph of a cycle Cp and the distance seidel energy of S(Cp), the complement of the even cycle C2p. | ||
| کلیدواژهها | ||
| Distance Seidel Matrix؛ Distance Seidel Spectrum؛ Distance Seidel Energy | ||
| مراجع | ||
[1] M. Aouchiche, P. Hansen, Distance spectra of graphs: a survey, Linear Algebra and its Appl., 458:301 -- 384, 2014. [2] F. Buckley and F. Harary, Distance in Graphs, Addison Wesley, 1990. [3] D. Cvetkovi\'c, M. Doob, and H. Sachs, Spectra of Graphs---Theory and Application, Johann Ambrosius Barth Verlag, 3 edition, 1995. [4] G.Indulal, Spectrum of two new joins of graphs and infinite families of integral graphs, Kragujevac Journal of Mathematics, 36:133 -- 139, 2012. [5] G.Indulal and R.Balakrishnan, Distance spectrum of indu - bala product of graphs, Journal of Graphs and Combinatorics}, 13:230-- 234, 2016. [6] G.Indulal and Dragan Stevanovi'c, The distance spectrum of corona and cluster of two graphs, International Journal of Graphs and Combinatorics, 12:186-192, 2015. [7] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forsch. Graz, 103:1--12, 1978. [8] A. Akbari and K. Chandra Das, Some properties of eigenvalues of the seidel matrix, Linear and Multilinear Algebra, 70(11):2150--2161, 2020. [9] M. Reza Oboudi, Energy and seidel energy of graphs, Commun. Math. Comput. Chem, 75(2):291--303, 2016. [10] A. Graovac, G. Jashari, and M. Strunje, On the distance spectrum of a cycle, Aplikace Matematiky, 30:286--290, 1985. [11] T. Haritha and A. V. Chithra, Distance Seidel matrix of a connected graph, arXiv.2210.05940v2 [math.CO], 28 Nov 2022. [13] G. Indulal, Sharp bounds on the distance spectral radius and the distance energy of graphs, Lin. Algebra Appl., 430:106 -- 113, 2009. [14] G. Indulal and I. Gutman, On the distance spectra of some graphs, Math. Commun., 13:123-131, 2008. [15] G. Indulal and I. Gutman, D-equienergetic self-complementary graphs, Kragujevac. J. Math., pages 123--131, 2009. [16] G. Indulal, I. Gutman and A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem., 60:461-472., 2008. [17] P. Krivka and N. Trinajstic, On the distance polynomial of a graph, Aplikace Matematiky, 28:357-363, 1983. [18] S. N Ruzieh and D. L. Powers, The distance spectrum of the path Pn and the first distance eigenvector of connected graphs, Linear and Multilinear Algebra, 28:75-81, 1990. [19] D. Stevanovi\'c, Large sets of long distance equienergetic graphs, Ars. Mathematica Contemporanea, 2:35-40, 2009. [20] D. Stevanovi\'c and G. Indulal, The distance spectrum and energy of the compositions of regular graphs, Appl. Math. Lett., 22:136-140, 2009. [21] G. Indulal, A. Vijayakumar, A note on energy of some graphs, MATCH Commun. Math.Comput. Chem., 59(2):269-271, 2008.
[22] I. Gopalapillai, D. C. Scaria, The distance related spectra of some subdivision related graphs,Journal of Computer Science and Applied Mathematics, 3(1):23-36, 2021. [23] G. Indulal, D. C. Scaria and X. Liu, The distance spectrum of the subdivision vertex join and subdivision edge join of two regular graphs, Discrete Math. Lett., 1: 36-41, 2019. | ||
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