Displaying similar documents to “Towards a geometric theory for left loops”

Multiples of left loops and vertex-transitive graphs

Eric Mwambene (2005)

Open Mathematics

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Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.

Median and quasi-median direct products of graphs

Boštjan Brešar, Pranava K. Jha, Sandi Klavžar, Blaž Zmazek (2005)

Discussiones Mathematicae Graph Theory

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Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.

The Cayley graph and the growth of Steiner loops

P. Plaumann, L. Sabinina, I. Stuhl (2014)

Commentationes Mathematicae Universitatis Carolinae

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We study properties of Steiner loops which are of fundamental importance to develop a combinatorial theory of loops along the lines given by Combinatorial Group Theory. In a summary we describe our findings.