A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic...

A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic...

We consider the problems of selection, routing and sorting on an n-star graph (with n! nodes), an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a '(k, l, k) chain network') of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs...

In this paper, we model the star interconnection network with a graph and present an innovative grid embedding into it. The embedding is speciically designed and optimized for image analysis solutions. Using the embedding, we outline the general approach for solving such problems on the star graph and analyze the data communication patterns involved in such solutions.

Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established.

A (finite or infinite) complete bipartite graph together with some end vertices all adjacent to a common vertex is called a complete bipartite graph with a horn. For any bipartite graph G, we show that G is the graph of a commutative semigroup with 0 if and only if it is one of the following graphs: star graph, two-star graph, complete bipartite graph, complete bipartite graph with a horn. We a...

This paper introduces a new interconnection network topology called the star-crossed cube (SCQ). The SCQ is observed to be superior to other contemporary networks in terms of various topological parameters such as diameter, cost, average distance, and message traffic density. The various performance metrics of the proposed network, including cost effectiveness and time-cost effectiveness, are f...

The star-connected cycles (SCC) graph was recently proposed as an attractive interconnection network for parallel processing, using a star graph to connect cycles of nodes. This paper presents embeddings of p-dimensional meshes into an n-dimensional SCC graph (1 p n), which have load 1, expansion 1, and dilation ranging from 1 to 3 + 2b(n ? 1)=2c + 2bn=4c (the dilation varies among mesh dimensi...

Let G be a finite graph of order n with an eigenvalue μ of multiplicity k. (Thus the μ-eigenspace of a (0, 1)-adjacency matrix of G has dimension k.) A star complement for μ in G is an induced subgraph G−X of G such that |X| = k and G−X does not have μ as an eigenvalue. An exceptional graph is a connected graph, other than a generalized line graph, whose eigenvalues lie in [−2,∞). We establish ...