Diameter of parallelogramic honeycomb torus

Xiaofan Yang, G.M. Megson, Yuanyan Tang, D.J. Evans
2005 Computers and Mathematics with Applications  
The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic honeycomb torus, which extends a known result about rhombic honeycomb torus. 1478 X. YANO et al. Stojmenovic [2] proposed three classes of
more » ... eycomb torus structures: hexagonal honeycomb torus, rectangular honeycomb torus, and parallelogramic honeycomb torus (which includes rhombic honeycomb torus as particular case). Cho [3] introduced the notion of generalized honeycomb tori, which includes the aforementioned three classes of honeycomb tori as special cases. Due to lower complexity, and hence, lower implementation cost compared with the classical torus networks, honeycomb torus networks have received significant attention [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] . In particular, Yang [10] gave an expression for the diameter of rhombic honeycomb torus. In this paper, we establish an expression for the diameter of a general parallelogramic honeycomb torus, which extends a known result about rhombic honeycomb torus.
doi:10.1016/j.camwa.2005.01.029 fatcat:kqpe5jl4ljdc5fje2vzzchrbne