آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 125 |
| تعداد مقالات | 1,585 |
| تعداد مشاهده مقاله | 1,755,040 |
| تعداد دریافت فایل اصل مقاله | 1,636,613 |
Distance spectra of neighbourhood corona of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 مرداد 1404 اصل مقاله (639.24 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30329.2417 | ||
| نویسندگان | ||
| K.D. Arathy* 1، 2؛ K. Pravas3 | ||
| 1Department of Mathematics, Sree Narayana College, Nattika, Kerala-680566, India | ||
| 2St. Joseph’s College (Autonomous) Irinjalakuda, Kerala-680121, Affiliated to University of Calicut, India | ||
| 3Department of Mathematics, Maharaja’s College, (Government Autonomous) Ernakulam, Kerala-682011, India | ||
| چکیده | ||
| The neighbourhood corona $G \star H$ of two graphs $G$ and $H$ is obtained by taking one copy of $G$ and $|V(G)|$ copies of $H$ and making all the neighbours of the $i^{\text{th}}$ vertex of $G$ adjacent with all the vertices in the $i^{\text{th}}$ copy of $H$. In this paper we describe the distance eigenvalues and corresponding eigenvectors of $G \star H$ in terms of the adjacency spectrum of $G$ and $H$ when $G$ is a regular triangle-free graph with diameter 2 and $H$ is regular. Several constructions are proposed using line graphs, iterated line graphs, double graphs, strong double graphs and complement graphs to obtain infinitely many distance non-cospectral pairs of distance equienergetic graphs and non-isomorphic pairs of distance cospectral graphs. Also we obtain the distance Laplacian spectrum of $G \star H$ in terms of the distance Laplacian spectrum of $G$ and Laplacian spectrum of $H$ when $G$ is a transmission regular triangle-free graph with diameter 2. Further we find the distance signless Laplacian spectrum of $G \star H$ in terms of the distance signless Laplacian spectrum of $G$ and signless Laplacian spectrum of $H$ when $G$ is a transmission regular triangle-free graph with diameter 2 and $H$ is regular. We also construct infinitely many non-isomorphic pairs of distance Laplacian cospectral graphs and distance signless Laplacian cospectral graphs. | ||
| کلیدواژهها | ||
| Distance spectrum؛ distance Laplacian spectrum؛ distance signless Laplacian spectrum؛ distance equienergetic graphs؛ distance cospectral graphs | ||
| مراجع | ||
|
[1] M. Aouchiche and P. Hansen, Two Laplacians for the distance matrix of a graph, Linear Algebra Appl. 439 (2013), no. 1, 21–33. https://doi.org/10.1016/j.laa.2013.02.030
[2] M. Aouchiche and P. Hansen, Distance spectra of graphs: A survey, Linear Algebra Appl. 458 (2014), 301–386. https://doi.org/10.1016/j.laa.2014.06.010
[3] F. Buckley, The size of iterated line graphs, Graph Theory Notes New York, 1993, pp. 33–36.
[4] D.M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs: Theory and Application, Academic Press, New York, 1980.
[5] R. Frucht and F. Harary, On the corona of two graphs, Aeq. Math. 4 (1970), 322–325. https://doi.org/10.1007/BF01844162
[6] R.L. Graham and H.O. Pollak, On the addressing problem for loop switching, Bell Syst. Tech. J. 50 (1971), no. 8, 2495–2519. https://doi.org/10.1002/j.1538-7305.1971.tb02618.x
[7] I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz. 103 (1978), 1–22.
[8] I. Gutman and B. Furtula, Survey of graph energies, Math. Interdiscip. Res. 2 (2017), no. 2, 85–129. https://doi.org/10.22052/mir.2017.81507.1057
[9] F. Harary, Graph Theory, Addison-Wesley Publishing Company, 1969.
[10] R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Topics in Matrix Analysis, Cambridge University Press, 1994.
[11] G. Indulal, The spectrum of neighborhood corona of graphs, Kragujev. J. Math. 35 (2011), no. 37, 493–500.
[12] G. Indulal, I. Gutman, and A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), no. 2, 461–472.
[13] X. Li, Y. Shi, and I. Gutman, Graph Energy, Springer, New York, 2012.
[14] H. Lin, J. Shu, J. Xue, and Y. Zhang, A survey on distance spectra of graphs, Adv. Math.(China) 50 (2021), no. 1, 29–76.
[15] X. Liu and P. Lu, Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae, Linear Algebra Appl. 438 (2013), no. 8, 3547–3559. https://doi.org/10.1016/j.laa.2012.12.033
[16] X. Liu and S. Zhou, Spectra of the neighbourhood corona of two graphs, Linear Multilinear Algebra 62 (2014), no. 9, 1205–1219. https://doi.org/10.1080/03081087.2013.816304
[17] E. Munarini, C.P. Cippo, A. Scagliola, and N.Z. Salvi, Double graphs, Discrete Math. 308 (2008), no. 2-3, 242–254. https://doi.org/10.1016/j.disc.2006.11.038 [18] S. Pirzada and H.A. Ganie, Spectra, energy and laplacian energy of strong double graphs, Mathematical Technology of Networks: Bielefeld, December 2013, Springer, 2015, pp. 175–189
[19] H.S. Ramane, H.B. Walikar, S.B. Rao, B.D. Acharya, P.R. Hampiholi, S.R. Jog, and I. Gutman, Spectra and energies of iterated line graphs of regular graphs, Appl. Math. Lett. 18 (2005), no. 6, 679–682. https://doi.org/10.1016/j.aml.2004.04.012 | ||
|
آمار تعداد مشاهده مقاله: 176 تعداد دریافت فایل اصل مقاله: 227 |
||