Edge Disjoint Hamiltonian Cycles in Gaussian Networks.

Gaussian networks are degree four symmetric networks and these are designed based on the concept of Gaussian integers. The Gaussian network can be described in terms of a generator $\alpha =a+bi$ <alternatives><inline-graphic xlink:type="simple" xlink:href="albader-ieq1-2409843.gif"/></alternatives>, where a$<alternatives><inline-graphic xlink:type="simple" xlink:href="albader-ieq2-2409843.gif"/> </alternatives> and b$<alternatives> <inline-graphic xlink:type="simple" xlink:href="albader-ieq3-2409843.gif"/></alternatives> are integers and <alternatives> <inline-graphic xlink:type="simple" xlink:href="albader-ieq4-2409843.gif"/></alternatives>. When $\gcd (a,b)=1$<alternatives><inline-graphic xlink:type="simple" xlink:href="albader-ieq5-2409843.gif"/></alternatives> , how to find edge disjoint Hamiltonian cycles has been shown before. In this paper for any generator $\alpha =a+bi,$<alternatives> <inline-graphic xlink:type="simple" xlink:href="albader-ieq6-2409843.gif"/></alternatives> even when $\gcd (a, b)=d > 1$<alternatives><inline-graphic xlink:type="simple" xlink:href="albader-ieq7-2409843.gif"/> </alternatives>, how to obtain two edge disjoint Hamiltonian cycles in these networks is described. [ABSTRACT FROM AUTHOR]