Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T07:56:46.435Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular graphs with regular neighborhoods

Published online by Cambridge University Press:  18 May 2009

Ľubomír Šoltés
Ľubomír Šoltés
Affiliation:
KNOM MFF Comenius University, 842 15 Bratislava, Czechoslovakia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 215 - 218
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

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.Behzad, M., Chartrand, G. and Lesniak-Foster, L., Graphs and digraphs, Prindle, Weber & Schmidt, 1979.Google Scholar
3.Fronček, L., Locally linear graphs, Math. Slov. 39 (1989), 3–6.Google Scholar
4.Nedela, R., private communication, 1989.Google Scholar
5.Šoltes, Ľ., Neighbourhoods in line graphs, submitted.Google Scholar
6.Zelinka, B., Polytopic locally linear graphs, Math. Slov. 38 (1988) 99–103.Google Scholar
7.Zykov, A. A., Problem 30, Theory of graphs and its applications, Proc. Symp. Smolenice 1963 (Academia Prague, 1964), 164–165.Google Scholar