آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 122 |
| تعداد مقالات | 1,538 |
| تعداد مشاهده مقاله | 1,628,302 |
| تعداد دریافت فایل اصل مقاله | 1,525,833 |
Spectral properties of eccentricity sum matrix of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 خرداد 1404 اصل مقاله (434.91 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30199.2355 | ||
| نویسندگان | ||
| Balkishbanu Khaji؛ Shahistha Hanif* ؛ K. Arathi Bhat | ||
| Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal-576-104, Karnataka, India | ||
| چکیده | ||
| The spectral properties of extended adjacency matrices possess high discriminating power and correlate well with various physicochemical properties and biological activities of organic compounds. In the current article, a detailed investigation of one of the extended adjacency matrices called the eccentricity sum matrix is undertaken. The eccentricity sum matrix of a graph G, denoted by A_(ε^c ) (G) is a real symmetric matrix that if i≠ j and v_i v_j∈ E(G), then the (i,j)^th- entry is e(v_i)+e(v_j) and zero otherwise, where e(v_i) is the eccentricity of vertex v_i. The properties like trace, principle minors, and eigenvalues of the eccentricity sum matrix are explored. Moreover, we present some bounds for spectral radius and energy. Also, the energy and spectrum of some classes of graphs like fan graphs, bi-star graphs, etc., and their complements are obtained. | ||
| کلیدواژهها | ||
| Eccentricity؛ Spectral radius؛ Cocktail party graph؛ Bi-star graph؛ Crown graph | ||
| مراجع | ||
|
[1] H. Alzer, On the Cauchy-Schwarz inequality, J. Math. Anal. Appl. 234 (1999), no. 1, 6–14. https://doi.org/10.1006/jmaa.1998.6252
[2] A.R. Ashrafi, T. Došlić, and M. Saheli, The eccentric connectivity index of TUC4C8 (R) nanotubes, MATCH Commun. Math. Comput. Chem 65 (2011), no. 1, 221–230.
[3] D.M. Batinetu-Giurgiu and O.T. Pop, A generalization of Radon’s inequality, Creative Math. Inf. 19 (2010), no. 2, 116–121.
[4] A.E. Brouwer and W.H. Haemers, Spectra of Graphs, Springer Science & Business Media, 2011.
[5] D. Cokilavany, Extended energy of some standard graphs, Malays. J. Math. Sci. 8 (2020), no. 02, 510–516. https://doi.org/10.26637/MJM0802/0032 [6] D.M. Cvetković, Graphs and their spectra, Publ. Elektroteh. Fak., Univ. Beogradu, Ser. (1971), no. 354/356, 1–50.
[7] K.C. Das, I. Gutman, and B. Furtula, On spectral radius and energy of extended adjacency matrix of graphs, Appl. Math. Comput. 296 (2017), 116–123. https://doi.org/10.1016/j.amc.2016.10.029
[8] K.C. Das and S.A. Mojallal, Relation between energy and (signless) Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem 74 (2015), no. 2, 359–366.
[9] C. Godsil and G.F. Royle, Algebraic Graph Theory, Springer Science & Business Media, 2013.
[10] S. Gupta, M. Singh, and A.K. Madan, Application of graph theory: Relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity, J. Math. Anal. Appl. 266 (2002), no. 2, 259–268. https://doi.org/10.1006/jmaa.2000.7243
[11] I. Gutman, Contribution to the problem of spectra of compound graphs, Publ. Inst. Math. 24 (1978), no. 38, 53–60.
[12] R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge university press, 1994.
[13] A. Ilić, Eccentric connectivity index, arXiv preprint arXiv:1103.2515 (2011).
[14] A. Ilić and I. Gutman, Eccentric connectivity index of chemical trees, arXiv preprint arXiv:1104.3206 (2011).
[15] G. Indulal, I. Gutman, and A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), no. 2, 461–472.
[16] M.J. Morgan, S. Mukwembi, and H.C. Swart, On the eccentric connectivity index of a graph, Discrete Math. 311 (2011), no. 13, 1229–1234. https://doi.org/10.1016/j.disc.2009.12.013.
[17] D.S. Revankar, M.M. Patil, B.S. Durgi, and S.R. Jog, On eccentricity sum energy of some graphs, J. Xian Univ. Archit. Technol. 8 (2020), no. 8, 120–127.
[18] D.S. Revankar, M.M. Patil, and H.S. Ramane, On eccentricity sum eigenvalue and eccentricity sum energy of a graph, Ann. Pure Appl. Math 13 (2017), 125–130. http://dx.doi.org/10.22457/apam.v13n1a12
[19] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), no. 1, 17–20. https://doi.org/10.1021/ja01193a005 [20] Y.Q. Yang, L. Xu, and C.Y. Hu, Extended adjacency matrix indices and their applications, J. Chem. Inf. Comput. Sci. 34 (1994), no. 5, 1140–1145. https://doi.org/10.1021/ci00021a020
[21] S. Yin, Investigation on spectrum of the adjacency matrix and Laplacian matrix of graph Gl, WSEAS Trans. Syst 7 (2008), no. 4, 362–372.
[22] B. Zhou and Z. Du, On eccentric connectivity index, arXiv preprint arXiv:1007.2235 (2010). | ||
|
آمار تعداد مشاهده مقاله: 181 تعداد دریافت فایل اصل مقاله: 235 |
||