Note on Integral Graphs and Digraphs
by
P. Híc
Trnava

A graph G is called integral if all the zeros of the characteristic polynomial P(G;x) are integers. A tree T is called balanced if the vertices at the same distance from the centre of T have the same degree.

Here we present that the problem of characterizing balanced integral trees of diameter 6 can be transformed to the problem to investigate solutions of Pell's diophantine equations.

We also investigate nonsymetric strong (strongly connected) integral digraphs. We give constructions of two families of nonsymetric strong integral digraphs of large diameter. Further, it is proved, that the spectrum of second of them consists of 0, +/- a, +/- b, +/- c, +/- d, for every a, b, c, d in N, b > a, a² >= c² + d².

Date received: May 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafd-10.