In this paper, we aim to embed a longest path between every two vertices of a star graph with at most n-3 random edge faults, where n is the dimension of the star graph. Since the star graph is regular of degree n1, n-3 (edge faults) is maximum in the worst case. We show that when n≥6 and there are n-3 edge faults, the star graph can embed a longest path between every two vertices, exclusive of...

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, ...

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...