The Mathematical Combinatorics (International Book Series)(ISBN 978-1-59973-146-9) is a fully refereed international book series, sponsored by the MADISof Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pagesapprox. per volume, which publishes original research papers and survey articles in all aspectsof Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics,non-euclidean geometry and topology and their applications to other sciences. Topics in detailto be covered are:Smarandache multi-spaces with applications to other sciences, such as those of algebraicmulti-systems, multi-metric spaces,· · · , etc.. Smarandache geometries;Differential Geometry; Geometry on manifolds;Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph andmap enumeration; Combinatorial designs; Combinatorial enumeration;Low Dimensional Topology; Differential Topology; Topology of Manifolds;Geometrical aspects of Mathematical Physics and Relations with Manifold Topology;Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatoricsto mathematics and theoretical physics;Mathematical theory on gravitational fields; Mathematical theory on parallel universes;Other applications of Smarandache multi-space and combinatorics.Generally, papers on mathematics with its applications not including in above topics arealso welcome.