We derive some properties of the star graph in this paper. In particular, we compute the number of nodes at distance i from a fixed node e in a star graph. To this end, a recursive formula is first obtained. This recursive formula is, in general, hard to solve for a closed form solution. We then study the relations among the number of nodes at distance i to node e in star graphs of different dimensions. This study reveals a very interesting relation among these numbers, which leads to a simple homogeneous linear recursive formula whose characteristic equation is easy to solve. Thus, we get a systematic way to obtain a closed form solution with given initial conditions for any fixed i. © 1995, OPA (Overseas Publishers Association).
CITATION STYLE
Qiu, K., & Akl, S. G. (1995). On Some Properties of the Star Graph. VLSI Design, 2(4), 389–396. https://doi.org/10.1155/1995/61390
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