Spectra of M-rooted product of graphs

References

• Cvetković D, Doob M, Sachs H. Spectra of graphs: theory and applications. New York: Academic Press; 1980.
   Google Scholar
• Nikiforov V. Merging the A- and Q-spectral theories. Appl Anal Discrete Math. 2017;11:81–107.
   Web of Science ®Google Scholar
• Cvetković D, Rowlinson P, Simić S. An introduction to the theory of graph spectra. Cambridge: Cambridge University Press; 2010.
   Google Scholar
• Mohar B. Some applications of Laplace eigenvalues of graphs. In:  Hahn G, Sabidussi G. (eds) Graph symmetry: NATO ASI Series (Series C: Mathematical and Physical Sciences),  Springer, Dordrecht 1997. p. 225–275.
   Google Scholar
• Barik S, Kalita D, Pati S, et al. Spectra of graphs resulting from various graph operations and products: a survey. Special Matrices. 2018;6(1):323–342.
   Web of Science ®Google Scholar
• Cui SY, Tian GX. The signless Laplacian spectrum of the (edge) corona of two graphs. Util Math. 2012;88:287–297.
   Web of Science ®Google Scholar
• Cui SY, Tian GX. The Kirchhoff index and Laplacian spectrum of coronae. Util Math. 2017;103:41–50.
   Web of Science ®Google Scholar
• Tian GX, Yu PK, Cui SY. The signless Laplacian state transfer in coronas. Linear Multilinear Algebra. doi:https://doi.org/10.1080/03081087.2019.1594669
   Google Scholar
• Hedetniemi S. On classes of graphs defined by special cutsets of lines. In: Many facets of graph theory. Proc. Conf. Western MiGammagan Univ., Kalamazoo, MI, 1968; Lect Notes Math. 1969;110:171–189.
   Google Scholar
• Gayathri M, Rajkumar R. Spectra of partitioned matrices and M-join of graphs (Communicated).
   Google Scholar
• Godsil CD, Mckay BD. A new graph product and its spectrum. Bull Aust Math Soc. 1978;18:21–28.
   Google Scholar
• Barrire L, Comellas F, Dalf C, et al. The hierarchical product of graphs. Discrete Appl Math. 2009;157:36–48.
   Web of Science ®Google Scholar
• Accardi L, Ben Ghorbal A, Obata N. Monotone independence, comb graphs and Bose-Einstein condensation. Inf Dimen Anal Quant Prob Relat. 2004;7(3):419–435.
   Web of Science ®Google Scholar
• Jakovac M. The k-path vertex cover of rooted product graphs. Discrete Appl Math. 2015;187:111–119.
   Web of Science ®Google Scholar
• Kuziak D, Yero IG, Rodrguez-Velzquez JA. Strong metric dimension of rooted product graphs. Int J Comput Math. 2016;93(8):1265–1280.
   Web of Science ®Google Scholar
• Zhu B-X, Wang Q. Unimodality of independence polynomials of rooted products of graphs. Proc R Soc Edinb A Math. 2019:1–13.
   Google Scholar
• Azari M, Iranmanesh A. Chemical graphs constructed from rooted product and their Zagreb indices. MATCH Commun Math Comput Chem. 2013;70:901–919.
   Web of Science ®Google Scholar
• Heydari A, Taeri B. On the characteristic polynomial of a special class of graphs and spectra of balanced trees. Linear Algebra Appl. 2008;429:1744–1757.
   Web of Science ®Google Scholar
• Maghsoudi M, Heydari A. On the signless Laplacian spectrum of rooted product of graphs. Discrete Math. Algorithm. Appl. 2018;10(6). Article no. 1850076 [11 pp.].
   Web of Science ®Google Scholar
• Golinskii L. Spectra of comb graphs with tails. arXiv:1904.06678v1.
   Google Scholar
• Schwenk AJ. Computing the characteristic polynomial of a graph. In: Graphs and combinatorics (Proc. Capital Conf., George Washington Univ., Washington, DC, 1973), Lect Notes Math. 1974:406:153–172.
   Google Scholar
• Barik S. On the Laplacian spectra of graphs with pockets. Linear Multilinear Algebra. 2008;56:481–490.
   Web of Science ®Google Scholar
• Barik S, Sahoo G. Results on Laplacian spectra of graphs with pockets. AKCE Int J Graphs Comb. 2018;15(1):79–87.
   Web of Science ®Google Scholar
• Cui SY, Tian GX. The spectra and the signless Laplacian spectra of graphs with pockets. Appl Math Comput. 2017;315:363–371.
   Web of Science ®Google Scholar
• Andrade E, Cardoso DM, Medina L, et al. Bethe graphs are attached to the vertices of a connected graph -- a spectral approach. Linear Multilinear Algebra. 2017;65(4):857–868.
   Web of Science ®Google Scholar
• Rojo O. Aα-spectrum of a graph obtained by copies of a rooted graph and applications; 2017. arXiv:1704.06730v1 [math.CO].
   Google Scholar
• Cardoso DM, Martins EA, Robbiano M, et al. Computing the Laplacian spectra of some graphs. Discrete Appl Math. 2012;160:2645–2654.
   Web of Science ®Google Scholar
• Cardoso DM, Martins EA, Robbiano M, et al. Copies of a rooted weighted graph attached to an arbitrary weighted graph and application. Electron J Linear Algebra. 2013;26:706–717.
   Web of Science ®Google Scholar
• Fan YZ, Li SD, Liang D. Spectral property of certain class of graphs associated with generalized Bethe trees and transitive graphs. Appl Anal Discrete Math. 2008;2:260–275.
   Web of Science ®Google Scholar
• Robbiano M, Gutman I, Jimnez R. Spectra of copies Bethe trees attached to path and applications. Bull Acad Serb Sci Arts (CI Sc Math Natur). 2008;137:59–81.
   Google Scholar
• Rojo O. The spectra of a graph obtained from copies of a generalized Bethe tree. Linear Algebra Appl. 2007;420:490–507.
   Web of Science ®Google Scholar
• Rojo O. Spectra of copies of a generalized Bethe tree attached to any graph. Linear Algebra Appl. 2009;431:863–882.
   Web of Science ®Google Scholar
• Rojo O, Medina L. Spectra of generalized Bethe trees attached to a path. Linear Algebra Appl. 2009;430:483–503.
   Web of Science ®Google Scholar
• Rojo O, Medina L. Spectra of weighted compound graphs of generalized Bethe trees. Electron J Linear Algebra. 2009;18:30–57.
   Web of Science ®Google Scholar
• Van Dam ER, Haemers WH. Which graphs are determined by their spectrum? Linear Algebra Appl. 2003;373:241–272.
   Web of Science ®Google Scholar
• Godsil CD, McKay BD. Constructing cospectral graphs. Aequationes Math. 1982;25:257–268.
   Google Scholar
• Hammer WH, Spence E. Enumeration of cospectral graphs. European J Combin. 2004;25(2):199–211.
   Web of Science ®Google Scholar
• Seress A. Large families of cospectral graphs. Des Codes Cryptogr. 2000;21:205–208.
   Web of Science ®Google Scholar
• Harary F, Schwenk AJ. Which graphs have integral spectra? Graphs combin. In: Proceedings of Capital Conference, Washington, DC, 1973. Lect Notes Math. 1974;406:45–51.
   Google Scholar
• Balińska K, Cvetković D, Radosavljević Z, et al. A survey on integral graphs. Univ Beograd Publ Elektrotehn Fak Ser Mat. 2003;13:42–65.
   Google Scholar
• Ahmadi O, Alon N, Blake I, et al. Graphs with integral spectrum. Linear Algebra Appl. 2009;430:547–552.
   Web of Science ®Google Scholar
• Horn RA, Johnson CR. Matrix analysis. Cambridge: Cambridge University Press; 1985.
   Google Scholar
• Wilansky A. The row-sums of the inverse matrix. Amer Math Monthly. 1951;58:614–615.
   Google Scholar
• Meyer CD. Matrix analysis and applied linear algebra. Philadelphia,PA: SIAM; 2000.
   Google Scholar
• Gantmacher FR. Matrizentheorie. New York: Springer; 1986.
   Google Scholar
• McLeman C, McNicholas E. Spectra of coronae. Linear Algebra Appl. 2011;435:998–1007.
   Web of Science ®Google Scholar
• Cui SY, Tian GX. The spectrum and the signless Laplacian spectrum of coronae. Linear Algebra Appl. 2012;437:1692–1703.
   Web of Science ®Google Scholar
• Rajkumar R, Gayathri M. Adjacency and Laplacian spectrum of generalized corona of graphs constrained by vertex subsets (Communicated).
   Google Scholar
• Tian GX, He JX, Cui SY. On the Laplacian spectra of some double join operations of graphs. Bull Malays Math Sci Soc. 2019;42(4):1555–1566.
   Web of Science ®Google Scholar
• Rojo O, Robbiano M, Cardoso DM, et al. Spectra of weighted rooted graphs having precribed subgraphs at some levels. Electron J Linear Algebra. 2011;22:653–671.
   Web of Science ®Google Scholar