Let G a group, a finite subset of G containing 1,A a non empty finite subset of G. Olson [6] proved that either. Using the connectivity of Cayley graphs, we have another proof of this result and show moreover that either if B = B−1 or B ∩ B−1 = {1}...
The Johnson graph $$J(v,k)$$ J ( v , k ) has, as vertices, the $$k$$ k -subsets of a $$v$$ v -set $$\mathcal {V}$$ V and as edges the pairs of $$k$$ k -subsets with intersection of size $$k-1$$ k - 1 . We introduce the notion of a neighbour-transitive code in $$J(v,k)$$ J ( v , k ) . This is a proper vertex subset $$\Gamma $$ Γ such that the subgroup $$G$$ G of graph ...
In this paper, we first give a classification of the family of 2-geodesic transitive abelian Cayley graphs. Let $$\Gamma $$Γ be such a graph which is not 2-arc transitive. It is shown that one of the following holds: (1) $$\Gamma \cong \mathrm{K}_{m[b]}$...
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