• Corpus ID: 53635149

The Second Subconstituent of some Strongly Regular Graphs

@article{Biggs2010TheSS,
  title={The Second Subconstituent of some Strongly Regular Graphs},
  author={Norman L. Biggs},
  journal={arXiv: Combinatorics},
  year={2010}
}
  • N. Biggs
  • Published 28 February 2010
  • Mathematics
  • arXiv: Combinatorics
This is a report on a failed attempt to construct new graphs that are strongly regular with no triangles. The approach is based on the assumption that the second subconstituent has an equitable partition with four parts. For infinitely many odd prime powers we construct a graph that is a plausible candidate for the second subconstituent. Unfortuantely we also show that the corresponding graph is strongly regular only when the prime power is 3, in which case the graph is already known. 
Conditions for the Parameters of the Block Graph of Quasi-Symmetric Designs
A quasi-symmetric design (QSD) is a 2-$(v,k,\lambda)$ design with intersection numbers $x$ and $y$ with $x 2(x+2)$ or if it is a $3$-design is proven. The computer algebra system Mathematica is used

References

SHOWING 1-10 OF 12 REFERENCES
Strongly regular graphs with no triangles
A simplified version of the theory of strongly regular graphs is developed for the case in which the graphs have no triangles. This leads to (i) direct proofs of the Krein conditions, and (ii) the
The Gewirtz Graph: An Exercise in the Theory of Graph Spectra
TLDR
It is proved that there is a unique graph (on 56 vertices) with spectrum 101235(-4)20 and its structure is examined, which turns out to be the Coxeter graph and the Sylvester graph.
Families of parameters for SRNT graphs
The feasibility conditions obtained in a previous report are refined, and used to determine several infinite families of feasible parameters for strongly regular graphs with no triangles. The methods
Problems in Algebraic Combinatorics
This is a list of open problems, mainly in graph theory and all with an algebraic flavour. Except for 6.1, 7.1 and 12.2 they are either folklore, or are stolen from other people.
Graphs with Maximal Even Girth
  • A. Gewirtz
  • Mathematics
    Canadian Journal of Mathematics
  • 1969
In this paper we examine the class G of simple undirected, connected graphs of diameter d > 1, girth 2d, and for any g ɛ G, if a pair of nodes are at distance d from each other, then that pair of
Designs, graphs, codes, and their links
TLDR
The authors have considerably reworked and expanded their earlier successful books on designs, graphs and codes, into an invaluable textbook that is accessible to any student with a background of undergraduate algebra.
Algebraic Graph Theory
TLDR
The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Some implications of the geometry of the 21-point plane
1. The projective plane p of points whose homogeneous coordinates belong to the Galois Field GF(22), or F4 as we will call it, consists of 21 points lying 5 on each of 21 lines; 5 lines pass through
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
...
...