Problems

φ(n, m) = n(m-1) + 1.

Assume that p nmid (m-1) and 2 ≤ m ≤ q+1/3. Then the cliques from Proposition 4.10 and Proposition 4.13 are maximal.

This partial choice of factors has a unique coherent extension to tildeA .

Do we always have ∂_v,G_B(A)≥ d μ(C(B))^1/d|A|^1-1/d ?

Is C_τ(A_+) always isomorphic to C_π(A_+) ? In other words, is there a bijection f:C_τ→ C_π that satisfies the condition d(x,y)∈ A_+⇔ d(f(x),f(y))∈ A_+?

Suppose we revised our definition of an s-partition so that each part was required to be 2-edge connected, except the small part. What degree of edge connectivity would be required to ensure the existence of an s-partition (if such a…

It is however conjectured that one of these constructions either “K-groupings” or “J-groupings” will yield a maximum independent set for a given I-graph.

Given a (2s + 1, k, λ) difference set D in a group G, and given a graph Γ of order k and size s, we ask whether it is possibile to label the vertices of Γ with the elements of D is such a way that every non-identity element of G may be…

Let G be a finite transitive group on Ω. If I_Ω(G) > 1/2, then I_Ω(G) = (q+1)/2q, for some q ∈ Q with 2q ∈ N.

Does our improved estimate for the edge isoperimetric inequality in the remark following Theorem 3.1 hold for general B, i.e. do we always have ∂_e,G_B(A)≥ d μ(Z(B))^1/d|A|^1-1/d ?

Assume that p nmid (m-1) and 2 ≤ m ≤ q+1/3. Then the cliques from Proposition 4.6 and Proposition 4.7 are maximal.

We conjecture that in the case of skips of j and j+1 we have in fact equality, and not just a lower bound using K-groupings.

Given an arbitrary rational number q ∈ [0,1] does there exist a relevant triple ⟨n,k,⋄⟩ such that q = Ψ(n,k,⋄)/n^k?

However, it is unknown whether all finite groups are connected 3-CI-groups, and it is conjectured in [15] that the answer is positive.