This paper presents a fault tolerant routing algorithm for the star graph. The suggested algorithm is based on the concept of unsafety vectors, originally proposed for hypercubes. In this algorithm, each node starts by computing a first level unsafety set, composed of the set of unreachable neighbors. It then performs some exchanges with its neighbors to determine the unsafety nodes. After that...

In this paper, three new node-ranking schemes for the star graph are presented and evaluated. These node-ranking schemes efficiently ‘‘embed’’ grids, pipelines, and reconfigurable multiple ring networks (cases of torus networks). These schemes improve similar known results on the star graph. They also allow efficient mapping of a wide class of algorithms into the star graph and hence facilitati...

‎A tree containing exactly two non-pendant vertices is called a double-star‎. ‎Let $k_1$ and $k_2$ be two positive integers‎. ‎The double-star with degree sequence $(k_1+1‎, ‎k_2+1‎, ‎1‎, ‎ldots‎, ‎1)$ is denoted by $S_{k_1‎, ‎k_2}$‎. ‎It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching‎. ‎In this paper‎, ‎we study the $S_{1,2}$-decomposit...

A star forest of a graph G is a spanning subgraph of G in which each component is a star. The minimum number of edges required to guarantee that an arbitrary graph, or a bipartite graph, has a star forest of size n is determined. Sharp lower bounds on the size of a largest star forest are also determined. For bipartite graphs, these are used to obtain an upper bound on the domination number in ...

Let Ω be a multiply Leibniz isometry equipped with a solvable, analytically natural graph. Recent developments in commutative analysis [5, 16] have raised the question of whether every hyper-partial graph is Noetherian and smoothly Poncelet. We show that

Software product line engineering has gained an exceptional attention and interest from scientific community in recent years as a consequence of reuse in mass software production. However, management of the common and variable characteristics and functionalities among a collection of software systems, which belong to the same application domain, is still a work in progress because it is neither...

Let G be a graph. The distance d(u,v) between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G)=12W(G)+12@?"{"u","v"}"@?"V"("G")d (u,v)^2. In this paper the hyper-Wiener indices of the Cartesian product, composition,...

We propose a new class of interconnection networks, called macro-star networks, which belong to the class of Cayley graphs and use the star graph as a basic building module. A macro-star network can have node degree that is considerably smaller than that of a star graph of the same size, and diameter that is sub-logarithmic and asymptotically within a factor of 1.25 from a universal lower bound...

We propose two fault-tolerant broadcasting schemes in star graphs. One of the schemes can tolerate up to n − 2 faults of the crash type in the n-star graph. The other scheme can tolerate up to ⌊ n−3d−1 2 ⌋ faults of the Byzantine type in the n-star graph, where d is the smallest positive integer satisfying n ≤ d!. Each of the schemes is designed for the single-port mode, and it completes the br...