Distinct Paths for the Star Graph

In this paper, we investigate the properties of cycles for node representation in the star graph. Cycles can be in any order. The position for each symbol in the ordinary cycle is fixed and the ordinary cycle can not be nested into any other cycle. However, cyclic shift operations on symbols in a none-ordinary cycle are allowed and none-ordinary cycle can be nested into any other cycle. The number of distinct paths for the star graph is determined using the combinatorial analysis.