Geodesic
A quasi-spectral characterization of strongly distance-regular graphs
The electronic journal of combinatorics, Tome 7 (2000)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

A graph $\Gamma$ with diameter $d$ is strongly distance-regular if $\Gamma$ is distance-regular and its distance-$d$ graph $\Gamma _d$ is strongly regular. The known examples are all the connected strongly regular graphs (i.e. $d=2$), all the antipodal distance-regular graphs, and some distance-regular graphs with diameter $d=3$. The main result in this paper is a characterization of these graphs (among regular graphs with $d$ distinct eigenvalues), in terms of the eigenvalues, the sum of the multiplicities corresponding to the eigenvalues with (non-zero) even subindex, and the harmonic mean of the degrees of the distance-$d$ graph.
DOI : 10.37236/1529
Classification : 05E30, 05C50, 05C75
Mots-clés : distance-regular graphs, strongly regular graph, spectral characterization 
@article{10_37236_1529,
     author = {M. A. Fiol},
     title = {A quasi-spectral characterization of strongly distance-regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1529},
     zbl = {0956.05103},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1529/}
}
TY  - JOUR
AU  - M. A. Fiol
TI  - A quasi-spectral characterization of strongly distance-regular graphs
JO  - The electronic journal of combinatorics
PY  - 2000
VL  - 7
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1529/
DO  - 10.37236/1529
ID  - 10_37236_1529
ER  - 
%0 Journal Article
%A M. A. Fiol
%T A quasi-spectral characterization of strongly distance-regular graphs
%J The electronic journal of combinatorics
%D 2000
%V 7
%U http://geodesic.mathdoc.fr/articles/10.37236/1529/
%R 10.37236/1529
%F 10_37236_1529
M. A. Fiol. A quasi-spectral characterization of strongly distance-regular graphs. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1529

Cité par Sources :