Short communications

The Euler Tour of $n$-Dimensional Manifold with Positive Genus

Cataranciuc Sergiu, Bujac-Leisz Mariana, Soltan Petru

Moldova State University, Faculty of Mathematics and Computer Science, Chişinău, Moldova

Abstract: In the paper [1] it is proved that abstract cubic $n$-dimensional torus [2] possesses a directed Euler tour of the same dimension. The result prompts to a new (virtual) device for transmission and reception of information. In the present paper it is shown that every abstract cubic $n$-dimensional manifold without borders, of positive genus possesses a $n$-dimensional directed Euler tour. This result has practical application.

Keywords and phrases: Abstract manifold, abstract cube, vacuum, directed Euler tour.

MSC: 18F15, 32Q60, 32C10

Received: 20.09.2007

Language: English

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