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**public sources and our publisher partners.**Grid embeddings are used not only to study the simulation capabilities of a parallel architecture but also to design its VLSI layout. In addition to dilation and congestion, wirelength is an… Expand

A minimum metric basis is a minimum set W of vertices of a graph G(V,E) such that for every pair of vertices u and v of G, there exists a vertex [email protected]?W with the condition that the length… Expand

The most popular bounded-degree derivative network of the hypercube is the butterfly network. The Benes network consists of back-to-back butterflies. There exist a number of topological… Expand

In this paper we solve the edge isoperimetric problem for circulant networks and consider the problem of embedding circulant networks into various graphs such as arbitrary trees, cycles, certain… Expand

In this paper we obtain a fundamental result to find the exact wirelength of 1-fault hamiltonian graphs into wheels and fans. Using this result we compute the exact wirelength of circulant graphs,… Expand

Distance properties of molecular graphs form an important topic in chemical graph theory. The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. A lot of… Expand

Let G ( V , E ) be a simple connected graph. A set S ? V is a power dominating set (PDS) of G, if every vertex and every edge in the system is observed following the observation rules of power system… Expand

The crossing number of a graph G is the minimum number of crossings of its edges among the drawings of G in the plane and is denoted by cr(G). Bhatt and Leighton proved that the crossing number of a… Expand

We consider the problem of embedding hypercubes into cylinders to minimize the wirelength. Further, we show that the edge isoperimetric problem solves the wirelength problem of regular graphs and, in… Expand

Hypercubes are a very popular model for parallel computation because of their regularity and the relatively small number of interprocessor connections. In this paper, we present an algorithm for… Expand