Regular graphs with regular neighborhoods
Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 215-218

Voir la notice de l'article provenant de la source Cambridge University Press

The existence of r-regular graphs such that each edge lies in exactly t triangles, for given integers t < r, is studied. If t is sufficiently close to r then each such connected graph has to be the complete multipartite graph. Relations to graphs with isomorphic neighborhoods are also considered.
Šoltés, Ľubomír. Regular graphs with regular neighborhoods. Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 215-218. doi: 10.1017/S0017089500008740
@article{10_1017_S0017089500008740,
     author = {\v{S}olt\'es, \v{L}ubom{\'\i}r},
     title = {Regular graphs with regular neighborhoods},
     journal = {Glasgow mathematical journal},
     pages = {215--218},
     year = {1992},
     volume = {34},
     number = {2},
     doi = {10.1017/S0017089500008740},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008740/}
}
TY  - JOUR
AU  - Šoltés, Ľubomír
TI  - Regular graphs with regular neighborhoods
JO  - Glasgow mathematical journal
PY  - 1992
SP  - 215
EP  - 218
VL  - 34
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008740/
DO  - 10.1017/S0017089500008740
ID  - 10_1017_S0017089500008740
ER  - 
%0 Journal Article
%A Šoltés, Ľubomír
%T Regular graphs with regular neighborhoods
%J Glasgow mathematical journal
%D 1992
%P 215-218
%V 34
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008740/
%R 10.1017/S0017089500008740
%F 10_1017_S0017089500008740

[1] 1.Antonucci, S., Su una generalizzazione dei grafi T e sulla regolarita quasi-forte. Riv. Mat. Univ. Parma (4) 13 (1987) 395–400. Google Scholar

[2] 2.Behzad, M., Chartrand, G. and Lesniak-Foster, L., Graphs and digraphs, Prindle, Weber &amp; Schmidt, 1979. Google Scholar

[3] 3.Fronček, L., Locally linear graphs, Math. Slov. 39 (1989), 3–6. Google Scholar

[4] 4.Nedela, R., private communication, 1989. Google Scholar

[5] 5.Šoltes, Ľ., Neighbourhoods in line graphs, submitted. Google Scholar

[6] 6.Zelinka, B., Polytopic locally linear graphs, Math. Slov. 38 (1988) 99–103. Google Scholar

[7] 7.Zykov, A. A., Problem 30, Theory of graphs and its applications, Proc. Symp. Smolenice 1963 (Academia Prague, 1964), 164–165. Google Scholar

Cité par Sources :