Eccentricity of the nodes of OTIS-cube and Enhanced OTIS-cube

摘要

In this paper we have classified the nodes of OTIS-cube based on theireccentricities. OTIS (optical transpose interconnection system) is a largescale optoelectronic computer architecture, proposed in \cite{KMKE92}, thatbenefit from both optical and electronic technologies. We show that radius anddiameter of OTIS-$Q_n$ is $n+1$ and $2n+1$ respectively. We also show thataverage eccentricity of OTIS-cube is $(3n/2+1)$. In \cite{D05}, a variant of OTIS-cube, called Enhanced OTIS-cube(E-OTIS-$Q_n$) was proposed. E-OTIS-$Q_n$ is regular of degree $n+1$ and maximally fault-tolerant. In this paper we have given a classification of the nodes of E-OTIS cube andderived expressions for the eccentricities of the nodes in each class. Based onthese results we show that radius and diameter of E-OTIS-$Q_n$ is $n+1$ and$\lfloor {4n+4/3} \rfloor$ respectively. We have also computed the averageeccentricity of E-OTIS-$Q_n$ for values of $n$ upto 20.