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A Smarandache multi-space is a union of different spaces equipped with some different structures for an integer , which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This is second part on multi-spaces. Many conceptions in graphs are generalized by Smarandache’s notion, such as multi-voltage graphs, Cayley graphs of a finite multi-group,multi-embedding of a graph in an -manifold, graph phase, , etc… New results are obtained.

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