On the characteristic polynomial and spectrum of Kragujevac trees

Author
Arak unversity of Technolgy
Abstract
The Kragujevac trees where are used in molecular graphs have been studed by researchers of graph Theory in last years. In this paper, we study the characteristic polynomial and spectrum of adjacency and Laplacian matrices of regular Kragujevac trees. As application of our obtained results, we compute a upper bound for spectral redius, energy of graph and kirchhoff index of Kragujevac trees.
Keywords

1. Hosseini S. A., Ahmadi M. B., Gutman I.,“ Kragujevac Trees with MinimalAtom-Bond Connectivity Index”, MATCH Commun. Math. Comput. Chem. 71 (2014) 5-20.



2. Cruz R., Gutman I., Rada J., “Topological indices of Kragujevac trees”, Proyecciones Journal of Mathematics, 33, No 4, (2014) 471-482.

3. lin H.,“On the Wiener Index of Trees with GivenNumber of Branching Vertices”, MATCH Commun. Math. Comput. Chem. 72 (2014) 310-314.

4. Heydari A., Taeri B.,“On the characteristic polynomial of a special class of graphs and spectra of balanced trees”, Linear Algebra and its Applications 429 (2008) 1744–1757.



5.Gutman I., Li X., Zhang,in J.,“Graph Energy,ed. by M.Dehmer, F.Emmert-Streib.Analysis of Complex Networks. From Biology to Linguistics (Wiley-VCH, Wein-heim,2009).



6. Gao X., Luo Y. F.,and Liu W. W.,“Kirc hhoff index in line , subdivision and total graphs of a regular graph”, Discrete Appl . Math.160 (2012) 560−565.