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Generalized graph cordiality

Oliver Pechenik, Jennifer Wise (2012)

Discussiones Mathematicae Graph Theory

Hovey introduced A-cordial labelings in [4] as a simultaneous generalization of cordial and harmonious labelings. If A is an abelian group, then a labeling f: V(G) → A of the vertices of some graph G induces an edge-labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. Research on A-cordiality...

Generating quasigroups for cryptographic applications

Czesław Kościelny (2002)

International Journal of Applied Mathematics and Computer Science

A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of...

Global left loop structures on spheres

Michael K. Kinyon (2000)

Commentationes Mathematicae Universitatis Carolinae

On the unit sphere 𝕊 in a real Hilbert space 𝐇 , we derive a binary operation such that ( 𝕊 , ) is a power-associative Kikkawa left loop with two-sided identity 𝐞 0 , i.e., it has the left inverse, automorphic inverse, and A l properties. The operation is compatible with the symmetric space structure of 𝕊 . ( 𝕊 , ) is not a loop, and the right translations which fail to be injective are easily characterized. ( 𝕊 , ) satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

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