Embedding an incomplete latin square in a latin square with a prescribed diagonal

Embedding a Latin square with transversal into a projective space

Article history: Received 20 May 2010 Available online xxxx

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...

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...

Rank 3 Latin square designs

A Latin square design whose automorphism group is transitive of rank at most 3 on points must come from the multiplication table of an elementary abelian p-group,

A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties