Geodesic
All graphs in which each pair of distinct vertices has exactly two common neighbors
Mathematica Bohemica, Tome 130 (2005) no. 1, pp. 101-105

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.
We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.
DOI : 10.21136/MB.2005.134219
Classification : 05C50, 05C75
Keywords: graphs; adjacency matrix; eigenvalues of a graph; common neighbours 
Stevanović, Dragan. All graphs in which each pair of distinct vertices has exactly two common neighbors. Mathematica Bohemica, Tome 130 (2005) no. 1, pp. 101-105. doi: 10.21136/MB.2005.134219
@article{10_21136_MB_2005_134219,
     author = {Stevanovi\'c, Dragan},
     title = {All graphs in which each pair of distinct vertices has exactly two common neighbors},
     journal = {Mathematica Bohemica},
     pages = {101--105},
     year = {2005},
     volume = {130},
     number = {1},
     doi = {10.21136/MB.2005.134219},
     mrnumber = {2128363},
     zbl = {1110.05064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134219/}
}
TY  - JOUR
AU  - Stevanović, Dragan
TI  - All graphs in which each pair of distinct vertices has exactly two common neighbors
JO  - Mathematica Bohemica
PY  - 2005
SP  - 101
EP  - 105
VL  - 130
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134219/
DO  - 10.21136/MB.2005.134219
LA  - en
ID  - 10_21136_MB_2005_134219
ER  - 
%0 Journal Article
%A Stevanović, Dragan
%T All graphs in which each pair of distinct vertices has exactly two common neighbors
%J Mathematica Bohemica
%D 2005
%P 101-105
%V 130
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134219/
%R 10.21136/MB.2005.134219
%G en
%F 10_21136_MB_2005_134219

[1] D. Cvetković, M. Doob, H. Sachs: Spectra of Graphs. Theory and Applications. Johann A. Barth, Heidelberg, 1995. | MR

[2] R. Diestel: Graph Theory. Second edition, Graduate Texts in Mathematics, vol. 173, Springer, New York, 2000. | MR | Zbl

[3] B. Zelinka: Graphs in which each pair of vertices has exactly two common neighbours. Math. Bohem. 118 (1993), 163–165. | MR | Zbl

Cité par Sources :