Geodesic
Bipartite graphs with five eigenvalues and pseudo designs
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 209-221.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A pseudo (v,k,$\lambda $)-design is a pair $(X, \mathcal{B})$ , where X is a v-set, and $\mathcal{B}=\{B_{1},\ldots,B_{v-1}\}$ is a collection of k-subsets (blocks) of X such that any two distinct B $_{ i }$,B $_{ j }$ intersect in $\lambda $ elements, and $0\leq \lambda $$\leq v - 1$. We use the notion of pseudo designs to characterize graphs of order n whose (adjacency) spectrum contains zero and $\pm \theta $ with multiplicity (n - 3)/2 where $0\theta\le\sqrt{2}$ . Meanwhile, partial results confirming a conjecture of O. Marrero on a characterization of pseudo (v,k,$\lambda $)-designs are obtained.
Keywords: spectrum of graph, pseudo design, BIBD, DS graph, cospectral graphs, incidence graph, subdivision of star 
@article{JAC_2012__36_2_a6,
     author = {Ghorbani, Ebrahim},
     title = {Bipartite graphs with five eigenvalues and pseudo designs},
     journal = {Journal of Algebraic Combinatorics},
     pages = {209--221},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a6/}
}
TY  - JOUR
AU  - Ghorbani, Ebrahim
TI  - Bipartite graphs with five eigenvalues and pseudo designs
JO  - Journal of Algebraic Combinatorics
PY  - 2012
SP  - 209
EP  - 221
VL  - 36
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a6/
LA  - en
ID  - JAC_2012__36_2_a6
ER  - 
%0 Journal Article
%A Ghorbani, Ebrahim
%T Bipartite graphs with five eigenvalues and pseudo designs
%J Journal of Algebraic Combinatorics
%D 2012
%P 209-221
%V 36
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a6/
%G en
%F JAC_2012__36_2_a6
Ghorbani, Ebrahim. Bipartite graphs with five eigenvalues and pseudo designs. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 209-221. http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a6/