journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2347 Some remarks on the index of a broom and equitable partitions Fonseca Carlos M. Da Kuwait College of Science and Technology, Doha District, Safat, 13133, Kuwait Faculty of Applied Mathematics and Informatics, Kliment Ohridski Blvd. 8, Technical University of Sofia, Sofia, 1000, Bulgaria Saraiva Paulo Faculty of Economics, Av. Dias da Silva, 165, University of Coimbra, Coimbra, 3004-512, Portugal Department of Mathematics, Centre for Mathematics, University of Coimbra, Coimbra, 3000-143, Portugal Centre for Business and Economics Research, Faculty of Economics, Av. Dias da Silva, 165, University of Coimbra, Coimbra, 3004-512, Portugal Yılmaz Fatih Department of Mathematics, Ankara Haci Bayram Veli University, Ankara, Turkey 29 6 2179 2188 27 03 2026

In this paper, we present an alternative and short proof for the expression of the index of a broom, based on equitable partitions and perturbed Toeplitz tridiagonal matrices. A similar general result for a double-broom is established.

 Equitable partitions Broom Eigenvalues Index Double-broom Trees Multiplicity Tridiagonal matrices access open retracted no