Automorphism free latin square graphs

Random Latin square graphs

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and seve...

Square-free Rings and Their Automorphism Group

Finite-dimensional square-freeK-algebras have been completely characterized by Anderson and D’Ambrosia as certain semigroup algebras A ∼= KξS over a square-free semigroup S twisted by some ξ ∈ Z (S,K), a two-dimensional cocycle of S with coefficients in the group of units K∗ of K. D’Ambrosia extended the definition of square-free to artinian rings with unity and showed every square-free ring ha...

On chromatic number of Latin square graphs

The chromatic number of a Latin square is the least number of partial transversals which cover its cells. This is just the chromatic number of its associated Latin square graph. Although Latin square graphs have been widely studied as strongly regular graphs, their chromatic numbers appear to be unexplored. We determine the chromatic number of a circulant Latin square, and find bounds for some ...

A class of orthogonal latin square graphs

An orthogonal latin square graph is a graph whose vertices are latin squares of the same order, adjacency being synonymous with orthogonality. We are interested in orthogonal latin square graphs in which each square is orthogonal to the Cayley table M of a group G and is obtained from M by permuting columns. These permutations, regarded as permutations of G, are orthomorphisms of G and the grap...

Square-free perfect graphs