Integral trees of diameter 6

Wang, L. and Broersma, H.J. and Hoede, C. and Li, X. and Still, G.J. (2007) Integral trees of diameter 6. Discrete Applied Mathematics, 155 (10). pp. 1254-1266. ISSN 0166-218X

PDF
Restricted to UT campus only: Request a copy
198Kb

Abstract:	A graph $G$ is called integral if all eigenvalues of its adjacency matrix $A(G)$ are integers. In this paper, the trees $T(p,q)\cdot T(r,m,t)$ and $K_{1,s}\cdot T(p,q)\cdot T(r,m,t)$ of diameter 6 are defined. We determine their characteristic polynomials. We also obtain for the first time sufficient and conditions for them to be integral. To do so, we use number theory and apply a computer search. New families of integral trees of diameter 6 are presented. Some of these classes are infinite. They are different from those in the existing literature. We also prove that the problem of finding integral trees of diameter 6 is equivalent to the problem of solving some Diophantine equations. We give a positive answer to a question of Wang et al. [Families of integral trees with diameters 4, 6 and 8, Discrete Appl. Math. 136 (2004) 349–362].
Item Type:	Article
Copyright:	© 2007 Elsevier
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/61773
Official URL:	http://dx.doi.org/10.1016/j.dam.2006.10.014
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Repository Staff Only: item control page

Metis ID: 241733