Displaying similar documents to “Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs”

Travel groupoids on infinite graphs

Jung Rae Cho, Jeongmi Park, Yoshio Sano (2014)

Czechoslovak Mathematical Journal

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The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set V and a binary operation * on V satisfying two axioms. We can associate a graph with a travel groupoid. We say that a graph G has a travel groupoid if the graph associated with the travel groupoid is equal to G . Nebeský gave a characterization of finite graphs having a travel groupoid. In this paper, we study travel groupoids on infinite...

Travel groupoids

Ladislav Nebeský (2006)

Czechoslovak Mathematical Journal

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In this paper, by a travel groupoid is meant an ordered pair ( V , * ) such that V is a nonempty set and * is a binary operation on V satisfying the following two conditions for all u , v ∈ V : ( u * v ) * u = u ; if ( u * v ) * v = u , then u = v . Let ( V , * ) be a travel groupoid. It is easy to show that if x , y ∈ V , then x * y = y if and only if y * x = x . We say that ( V , * ) is on a (finite or infinite) graph G if V ( G ) = V and E ( G ) = { { u , v } u , v ∈ V and u ≠ u * v = v } . Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.

Canonical Objects in Classes of (n, V)-Groupoids

Celakoska-Jordanova, Vesna (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: 03C05, 08B20 Free algebras are very important in studying classes of algebras, especially varieties of algebras. Any algebra that belongs to a given variety of algebras can be characterized as a homomorphic image of a free algebra of that variety. Describing free algebras is an important task that can be quite complicated, since there is no general method to resolve this problem. The aim of this work is to investigate classes of groupoids, i.e. algebras...

Categories, groupoids, pseudogroups and analytical structures

W. Waliszewski

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CONTENTSIntroduction................................................................................................................................................. 3I. TERMS AND NOTATION....................................................................................................................... 5II. GROUPOIDS AND CATEGORIES...................................................................................................... 61. The notion of groupoid............................................................................................................................