In this paper, we construct intriguing sets in five classes of strongly regular graphs defined on nonisotropic points finite classical polar spaces, and determine their intersection numbers.

We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V |) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that re...

It is well-known that any nite simple graph ? is an induced sub-graph of some exponentially larger strongly regular graph ? (e.g. 2, 8]). No general polynomial-size construction has been known. For a given-nite simple graph ? on v vertices we present a construction of a strongly regular graph ? on O(v 4) vertices that contains ? as its induced sub-graph. A discussion is included of the size of ...

We construct strongly walk-regular graphs as coset of the duals codes with three non-zero homogeneous weights over $${\mathbb {Z}}_{p^m},$$ for p a prime, and more generally chain rings depth m, residue field size q, prime power. In case $$p=m=2,$$ strong necessary conditions ( diophantine equations) on weight distribution are derived, leading to partial classification in modest length. Infinit...