𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Second neighbourhoods of strongly regular graphs

✍ Scribed by A.D. Gardiner; C.D. Godsil; A.D. Hensel; Gordon F. Royle

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
723 KB
Volume
103
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Some antipodal

distance-regular graphs of diameter three arise as the graph induced by the vertices at distance two from a given vertex in a strongly regular graph. We show that if every vertex in a strongly regular graph G has this property, then G is the noncollinearity graph of a special type of semipartial geometry.

As these semipartial geometries have all been classified, we obtain a list of the antipodal distance-regular graphs of diameter three that can arise in this way.

πŸ“œ SIMILAR VOLUMES

Distance regular graphs of diameter 3 an
Distance regular graphs of diameter 3 and strongly regular graphs
✍ A.E Brouwer πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 124 KB

In [1] N.L. Biggs mentions two parameter sets for distance regular graphs that are antipodal covers of a complete graph, for which existence of a corresponding graph was unknown. Here we settle both cases by proving that one does not exist, while there are exactly two nonisomorphic solutions to the

New families of strongly regular graphs
New families of strongly regular graphs
✍ Yury J. Ionin; Hadi Kharaghani πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 116 KB

## Abstract We apply symmetric balanced generalized weighing matrices with zero diagonal to construct four parametrically new infinite families of strongly regular graphs. Β© 2003 Wiley Periodicals, Inc. J Combin Designs 11: 208–217, 2003; Published online in Wiley InterScience (www.interscience.wil

On regular and strongly-regular self-com
On regular and strongly-regular self-complementary graphs
✍ S.B. Rao πŸ“‚ Article πŸ“… 1985 πŸ› Elsevier Science 🌐 English βš– 589 KB

In this paper we solve 3 of the 6 problems of A. Kotzig on regular and strongly-regular self-complementary graphs, mentioned in "Graph Theory and Related Topics" edited by J.A.

On strongly regular self - complementary
On strongly regular self - complementary graphs
✍ Sergio Ruiz πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 133 KB πŸ‘ 1 views

## Abstract It is shown that certain conditions assumed on a regular self‐complementary graph are not sufficient for the graph to be strongly regular, answering in the negative a question posed by Kotzig in [1].