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Rosenbloom and Tsfasman introduced a new metric (RT metric) which is a generalization of the Hamming metric. In this paper we study the distance graphs of spaces $Z_q^n$ and $S_n$ with Rosenbloom -Tsfasman metric. We also describe the degrees of vertices, components and the chromatic number of these graphs., Comment: This paper has been modified. 4 pages

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B contained in A which is embedded with a stronger structure S. These types of structures occur in our everyday life, that's why we study them in this book. Thus, as a particular case: A Smarandache semigroup is a semigroup A which has a proper subset B contained in A that is a group (with respect to the same binary operation on A)., 93 pages, 7 chapters and hundreds of new definitions