A proper coloring of the vertices of a graph is called a star coloring if every two color classes induce a star forest. Star colorings are a strengthening of acyclic colorings, i.e., proper colorings in which every two color classes induce a forest. We show that every acyclic k-coloring can be refined to a star coloring with at most (2k2 − k) colors. Similarly, we prove that planar graphs have ...

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also bee...

In this paper, we propose a specific structure in the star graph for local diagnosis under the PMC model. We design an adaptive local diagnosis algorithm for a star graph Sn. We prove that Sn is (n − 1)-diagnosable with our proposed algorithm under the PMC model. Moreover, with our algorithm, a diagnosis is completed in three test rounds.

The problem of solving a linear system of equations is widely encountered in many fields of science and engineering. In this paper, we present a parallel algorithm to solve the above problem on a star graph. The proposed solution (i) is based on a variant of the Gaussian elimination algorithm (GE) called the successive Gaussian elimination algorithm (SGE) (IEE Proc. Comput. Digit. Tech. 143 (4)...

Let G be a graph with chromatic number (G) and maximum degree (G). A star colouring of G is a function that assigns a colour to each vertex such that adjacent vertices receive distinct colours, and there is no bichromatic 4-vertex path. The star chromatic number st(G) is the minimum number of colours in a star colouring of G. Star colourings of subdivisions of graphs are investigated. Let G0 be...

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.

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...