In this research, another version of the star cube called the generalized-star cube, GSC(n, k,m), is presented as a three level interconnection topology. GSC(n, k,m) is a product graph of the (n, k)-star graph and the m-dimensional hypercube (m-cube). It can be constructed in one of two ways: to replace each node in an m-cube with an (n, k)-star graph, or to replace each node in an (n, k)-star ...

it is well know that any three impedances or admittances connected into each other in a star form can be easily transformed to a new three impedances or admittances connected into each other in a mesh form. in this paper a generalization of this fact is established and it is shown that in an n + 1 node network which is connected in a form it is always possible to eliminate the center node and o...

A star k-coloring is a proper k-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the vertex set into a 2-independent set and a forest; such a partition is called an I,F-partition. We use a combination of potential functions and discharg...

This work develops a novel general routing algorithm, which is a routing function, for constructing a container of width n 1 between any pair of vertices in an (n, k)-star graph with connectivity n 1. Since the wide diameters in an (n, n 1)-star graph and an (n, 1)-star graph have been derived by Lin et al. (2004), this work only addresses an (n, k)-star with 2 k n 2. The length of the longest ...

| The star-connected cycles (SCC) graph was recently proposed as an alternative to the cube-connected cycles (CCC) graph, using a star graph to connect cycles of nodes rather than a hypercube. This paper presents an analysis of broadcasting algorithms for SIMD and MIMD SCCs, covering both one-port and multiple-port versions. We show that O(n log n) one-port broadcasting algorithms that have bee...

A proper coloring of the vertices of a graph is called a star coloring if the union of every two color classes induce a star forest. The star chromatic number χs(G) is the smallest number of colors required to obtain a star coloring of G. In this paper, we study the relationship between the star chromatic number χs(G) and the maximum average degree Mad(G) of a graph G. We prove that: 1. If G is...

Objectives: To identify a new family of Arithmetic sequential graceful graphs. Methods: The methodology involves mathematical formulation for labeling the vertices given graph and subsequently establishing that these formulations give rise to arithmetic labeling. Findings: In this study, we analyzed some star related graphs namely Star graph, Ustar, t-star, double proved possess Novelty: Here, ...

The purpose of the paper is to provide an answer to a long standing problem to compute the distance distribution among the nodes in a star graph, i.e., to compute the exact number of nodes at a distance k from the identity node in a star graph where k varies from 0 to the diameter of the graph. A star graph is a Cayley graph like the hypercubes; for a hypercube Qn, there are exactly ` n r ́ node...

In this note we show that the concept of incidence coloring introduced in [BM] is a special case of directed star arboricity, introduced in [AA]. A conjecture in [BM] concerning asmyptotics of the incidence coloring number is solved in the negative following an example in [AA]. We generalize Theorem 2.1 of [AMR] concerning the star arboricity of graphs to the directed case by a slight modificat...

We investigate synchronization in the Kuramoto model with noise on a star graph. By revising case of complete graph, we propose closed form self-consistency equation for conventional order parameter and generalize it Using obtained equation, demonstrate that there is crossover between abrupt at small continuous phase transition quite large noise. probe this numerically analytically.