Embedding crossed cube into diverse product graphs and tree-derived architectures

期刊论文
发表日期：

2025年9月6日

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Paul Immanuel,
A. Berin Greeni

摘要

The embedding of graphs plays a vital role in simulating parallel architectures into other parallel topologies. Out of all parallel computing architectures in super-computing, hypercube, and its variants cannot be ignored because of the desirable, easily implementable, and applicable properties. One such variant of hypercube is the crossed cube \(CQ^r\) . With exponential growth in the layout of VLSI designs, the concept of embedding has attained paramount importance. Crossed cube, a highly cited one among the variants of hypercube is explored with respect to embedding in this work. As a sequel, we derive the exact wirelength of embedding crossed cube into certain tree-derived architectures, corona product of a path on \(2^{r-1}\) nodes into an isolated node (comb), Cartesian product of path on 2 nodes into a path on \(2^{r-1}\) nodes (ladder) and path (MinLA).