In this paper we show that for any fusion \(\mathcal {B}\) of an association scheme {A}\), the generalized Hamming \(H(n,\mathcal {B})\) is a nontrivial {A})\). We analyze case where {A}\) on strongly-regular graph, and determine parameters all graphs which scheme, \(H(2,\mathcal {A})\), has extra fusions, in addition to one arising from trivial {A}\).

We give simple arithmetic conditions that force the Sylow p -subgroup of critical group a strongly regular graph to take specific form. These depend only on parameters ( v , k λ μ ) under consideration. many examples, including how theory can be used compute Conway's 99-graph and an elementary argument no s r g 28 9 0 4 exists.

A spread of a strongly regular graph is a partition of the vertex set into cliques that meet Delsarte's bound (also called Hoffman's bound). Such spreads give rise to colorings meeting Hoffman's lower bound for the chromatic number and to certain imprimitive three-class association schemes. These correspondences lead to conditions for existence. Most examples come from spreads and fans in (part...

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 use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the first two cases, we compute the spectrum explicitly and show that it is determined by the spectrum of the adjacency matrix of the original graph. We then show ...

By Seidel’s switching, we construct new strongly regular graphs with parameters (276, 140, 58, 84). In this paper, we simplify the known switching theorem due to Bose and Shrikhande as follows. Let G = (V,E) be a primitive strongly regular graph with parameters (v, k, λ, μ). Let S(G,H) be the graph from G by switching with respect to a nonempty H ⊂ V . Suppose v = 2(k − θ1) where θ1 is the nont...

In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that runs in time exp{Õ(n 13 )} (this bound was recently improved to exp{Õ(n 15 )} [5]). It has since been an open question to remove the requirement that the graph...

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.