Abstract Strongly walk regular graphs (SWRGs or s -SWRGs) form a natural generalization of strongly (SRGs) where paths length 2 are replaced by . They can be constructed as coset the duals projective three-weight codes whose weights satisfy certain equation. We provide classifications feasible parameters these in binary and ternary case for medium size code lengths. For case, divisibility is in...

A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension of Γ is the smallest size of a resolving set for Γ. A graph is distance-regular if, for any two vertices u, v at each distance i, the number of neighbours of v at each possible distance from u (i.e. i−1, i or i...

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is introduced which is very simple and easy to implement, but very efficient in discriminating non-isomorphic graphs, in practice. This method does not need any ...

We present 15 new partial difference sets over 4 non-abelian groups of order 100 and 2 new strongly regular graphs with intransitive automorphism groups. The strongly regular graphs and corresponding partial difference sets have the following parameters: (100,22,0,6), (100,36,14,12), (100,45,20,20), (100,44,18,20). The existence of strongly regular graphs with the latter set of parameters was a...

The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in ...

A graph is 3-e.c. if for every 3-element subset S of the vertices, and for every subset T of S, there is a vertex not in S which is joined to every vertex in T and to no vertex in S \ T. Although almost all graphs are 3-e.c., the only known examples of strongly regular 3-e.c. graphs are Paley graphs with at least 29 vertices. We construct a new infinite family of 3-e.c. graphs, based on certain...