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VLSI Design
Volume 2 (1995), Issue 4, Pages 389-396
http://dx.doi.org/10.1155/1995/61390

On Some Properties of the Star Graph

1Command and Control Division, Defence Research Establishment Valcartier (DREV), 2459 Pie XI, Courcelette, G0A 1R0, Canada
2Department of Computing and Information Science, Queen's University, Kingston K7L 3N6, Ontario, Canada

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.