Recently, it has been shown that a connected graph $\Gamma$ with $d+1$ distinct eigenvalues and odd-girth $2d+1$ is distance-regular. The proof of this result was based on the spectral excess theorem. In this note we present an alternative and more direct proof which does not rely on the spectral excess theorem, but on a known characterization of distance regular graphs in terms of the predistance polynomial of degree $d$.
@article{10_37236_2289,
author = {Edwin R. van Dam and Miquel Angel Fiol},
title = {A short proof of the odd-girth theorem},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {3},
doi = {10.37236/2289},
zbl = {1253.05098},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2289/}
}
TY - JOUR
AU - Edwin R. van Dam
AU - Miquel Angel Fiol
TI - A short proof of the odd-girth theorem
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2289/
DO - 10.37236/2289
ID - 10_37236_2289
ER -
%0 Journal Article
%A Edwin R. van Dam
%A Miquel Angel Fiol
%T A short proof of the odd-girth theorem
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2289/
%R 10.37236/2289
%F 10_37236_2289
Edwin R. van Dam; Miquel Angel Fiol. A short proof of the odd-girth theorem. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2289
