Abstract
A tree can be classified in two types, according to the existence or not of zero entries of its Fiedler vector. In this paper, the type of broom trees \(T_{n,k}\) of order n for particular values of k is determined.
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References
Abreu N, Fritscher E, Justel C, Kirkland S (2017) On the characteristic set, centroid, and centre for a tree. Linear Multilinear Algebra 65(10):2046–2063
Andrade E, Ciardo L, Dahl G (2022) Perron values and classes of trees. Linear Algebra Appl 639:135–158
Aouchiche M, Hansen P (2010) A survey of automated conjectures in spectral graph theory. Linear Algebra Appl 432:2293–2322
Brualdi RA, Goldwasser JL (1984) Permanent of the Laplacian matrix of trees and bipartite graphs. Discrete Math 48:1–21
Fallat S, Kirkland S (1998) Extremizing algebraic connectivity subject to graph theoretic constraints. Electron J Linear Algebra 3:48–74
Fiedler MM (1973) Algebraic connectivity of graphs. Czvchoslov Math J 23:298–305
Fiedler MM (1975) A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czechoslov Math J 25:607–618
Grone R, Merris R (1990) Ordering trees by algebraic connectivity. Graphs Combin 6:229–237
Horn RA, Johnson CR (1992) Matrix analysis. Cambridge University Press, New York
Kirkland S (1999) Constructions for type I trees with nonisomorphic Perron branches. Czechoslov Math J 49(3):617–632
Kirkland S, Neumann M, Shader BL (1996) Characteristic vertices of weighted trees via perron values. Linear Multilinear Algebra 40(4):311–325
Lin W, Guo X (2007) On the largest eigenvalues of trees with perfect matchings. J Math Chem 42:1057–1067
Merris R (1987) Characterisctic vertices of trees. Linear Multilinear Algebra 22:115–131
Pandey D, Patra KL (2022) Different central parts of trees and their pairwise distances. Linear Multilinear Algebra 70(19):3790–3802
Patra KL (2007) Maximizing the distance between center, centroid and characteristic set of a tree. Linear Multilinear Algebra 55(4):381–397
Xue J, Liu R, Yu G, Shu J (2020) The multiplicity of \(A_{\alpha }\)-eigenvalues of graphs. Electron J Linear Algebra 36:645–657
Yan W, Ye L (2005) On the minimal energy of trees with a given diameter. Appl Math Lett 18:1046–1052
Acknowledgements
The authors would like to thank the referees for a careful reading of the manuscript and for many valuable suggestions. This work was partially financed by CAPES, Coordenação de Aperfeiçoamento de Pessoal do Nível Superior-Brasil, Finance Code 001.
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Communicated by Marcos Eduardo Valle.
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Felisberto Traciná Filho, D., Justel, C.M. About the type of broom trees. Comp. Appl. Math. 42, 364 (2023). https://doi.org/10.1007/s40314-023-02497-2
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DOI: https://doi.org/10.1007/s40314-023-02497-2