R. Sundara Rajan

EMBEDDING VARIANTS OF HYPERCUBES WITH DILATION 2

Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of interconnection networks. In this paper, we introduce a technique to obtain a lower bound for the dilation of an embedding. Moreover, we give algorithms for embedding variants of hypercubes with dilation 2 proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding folded hypercubes and augmented cubes into hypercubes.

Average Distance in Interconnection Networks via Reduction Theorems for Vertex-Weighted Graphs

Average distance is an important parameter for measuring the communication cost of computer networks. A popular approach for its computation is to first partition the edge set of a network into convex components using the transitive closure of the Djoković-Winkler’s relation and then to compute the average distance from the respective invariants of the components. In this paper we refine this idea further by shrinking the quotient graphs into smaller weighted graph called reduced graph, so that the average distance of the original graph is obtained from the reduced graphs. We demonstrate the significance of this technique by computing the average distance of butterfly and hypertree architectures. Along the way a computational error from [European J. Combin. 36 (2014) 71–76] is corrected.

A Lower Bound for Dilation of an Embedding

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. In this paper, we introduce a technique to obtain a lower bound for dilation of an embedding. Moreover, we give algorithms to compute exact dilation of embedding circulant network into a triangular grid, Tower of Hanoi graph and Sierpinski gasket graph, proving that the lower bound obtained is sharp.

Bothway embedding of circulant network into grid

Graph embedding is an important technique that maps a guest graph into a host graph, usually an interconnection network. In this paper, we compute the dilation and wirelength of embedding circulant network into grid and vice versa.

Domination in certain chemical graphs

Domination theory is required for encryption of binary string into a DNA sequence. A dominating set of a graph

A note on minimum linear arrangement for BC graphs

G=(V,E)

A note on the locating-total domination in graphs

G=(V,E) is a subset