ON SOME PROPERTIES OF THE STAR GRAPH

We derive some properties of the star graph in this paper. In particul ar, we compute the number of nodes at distance i from a fixed node e i n a star graph. To this end, a recursive formula is first obtained. Th is recursive formula is, in general, hard to solve for a closed form s olution. We then study the relations among the number of nodes at dist ance i to node e in star graphs of different dimensions. This study re veals a very interesting relation among these numbers, which leads to a simple homogeneous linear recursive formula whose characteristic equ ation is easy to solve. Thus, we get a systematic way to obtain a clos ed form solution with given initial conditions for any fixed i.