On the Characteristic Polynomial and Spectrum of the Terminal Distance Matrix of Kragujevac Trees

Document Type : Research Paper


Department of Science, Arak University of Technology, Arak, Iran


In this paper‎, ‎the characteristic polynomial and the spectrum of the terminal distance matrix for some Kragujevac trees is computed. ‎As Application‎, ‎we obtain an upper bound and a lower bound for the spectral radius of the terminal distance matrix of the Kragujevac trees‎.


1. I. Gutman, B. Furtula and M. Petrović, Terminal Wiener index, J. Math. Chem. 46 (2009) 522–531.
2. B. Horvat, T. Pisanski and M. Randić, Terminal polynomials and star-like graphs, Match Commun. Math. Comput. Chem. 60 (2008) 493–512.
3. M. Randić, J. Zupan and D. Vikić-Topić, On representation of proteins by star-like graphs, J. Mol. Graph. Modell. 26 (2007) 290–305.
4. E. A. Smolenskii, E. V. Shuvalova, L. K. Maslova, I. V. Chuvaeva and M. S. Molchanova, Reduced matrix of topological distances with a minimum number of independent parameters: distance vectors and molecular codes, J. Math. Chem. 45 (2009) 1004 –1020.
5. D. Xiaotie and J. Zhang, Equiseparability on terminal Wiener index, Appl. Math. Letters 25 (3) (2012) 580–585.
6. R. Cruz, I. Gutman and J. Rada, Topological indices of Kragujevac trees, Proyecciones J. Math. 33 (4) (2014) 471–482.
7. S. A. Hosseini, M. B. Ahmadi and I. Gutman, Kragujevac trees with minimal atom-bond connectivity index, Match Commun. Math. Comput. Chem. 71 (2014) 5–20.
8. I. Gutman, Kragujevac trees and their energy, Sci. Publ. State Univ. Novi Pazar Ser. A: Appl. Math. Inform. and Mech. 6 (2) (2014) 71–79.
9. A. Heydari and B. Taeri, On the characteristic polynomial of a special class of graphs and spectra of balanced trees, Linear Algebra Appl. 429 (2008) 1744–1757.