Hyper-star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

2015 ◽  
Vol 27 (16) ◽  
pp. 4186-4193 ◽  
Author(s):  
F. Zhang ◽  
K. Qiu ◽  
J. S. Kim
Keyword(s):  
Topological Properties ◽  
Star Graphs ◽  
Broadcasting Algorithm

scholarly journals Topological properties of star graphs

1993 ◽  
Vol 25 (12) ◽  
pp. 87-98 ◽  
Author(s):  
Sumit Sur ◽  
Pradip K. Srimani
Keyword(s):  
Topological Properties ◽  
Star Graphs

Fault Tolerance on Star Graphs

1997 ◽  
Vol 08 (02) ◽  
pp. 127-142 ◽  
Author(s):  
Shuo-Cheng Hu ◽  
Chang-Biau Yang
Keyword(s):  
Fault Tolerance ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Constant Time ◽  
Multiprocessor Systems ◽  
Star Graph ◽  
Cycle Structure ◽  
Star Graphs ◽  
Broadcasting Algorithm

The capability of fault tolerance is one of the advantages of multiprocessor systems. In this paper, we prove that the fault tolerance of an n-star graph is 2n-5 with restriction to the forbidden faulty set. And we propose an algorithm for examining the connectivity of an n-star graph when there exist at most 2n - 4 faults. The algorithm requires O(n2 log n) time. Besides, we improve the fault-tolerant routing algorithm proposed by Bagherzadeh et al. by calculating the cycle structure of a permutation and the avoidance of routing message to a node without any nonfaulty neighbor. This calculation needs only constant time. And then, we propose an efficient fault-tolerant broadcasting algorithm. When there is no fault, our broadcasting algorithm remains optimal. The penalty is O(n) if there exists only one fault, and the penalty is O(n2) if there exist at most n - 2 faults.

scholarly journals Some topological properties of star graphs: The surface area and volume

2009 ◽  
Vol 309 (3) ◽  
pp. 560-569 ◽  
Author(s):  
Navid Imani ◽  
Hamid Sarbazi-Azad ◽  
Selim G. Akl
Keyword(s):  
Surface Area ◽  
Topological Properties ◽  
Star Graphs ◽  
Area And Volume

scholarly journals Design and Analysis of a Symmetric Log Star Graph with a Smaller Network Cost Than Star Graphs

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 981
Author(s):  
Jung-Hyun Seo ◽  
Hyeong-Ok Lee
Keyword(s):  
Parallel Computing ◽  
Computer Science ◽  
Regular Graph ◽  
Connected Graph ◽  
Routing Algorithm ◽  
Star Graph ◽  
Topological Properties ◽  
Star Graphs ◽  
Network Cost ◽  
Network Costs

Graphs are used as models to solve problems in fields such as mathematics, computer science, physics, and chemistry. In particular, torus, hypercube, and star graphs are popular when modeling the connection structure of processors in parallel computing because they are symmetric and have a low network cost. Whereas a hypercube has a substantially smaller diameter than a torus, star graphs have been presented as an alternative to hypercubes because of their lower network cost. We propose a novel log star (LS) that is symmetric and has a lower network cost than a star graph. The LS is an undirected, recursive, and regular graph. In LSn, the number of nodes is n! while the degree is 2log2n − 1 and the diameter is 0.5n(log2n)2 + 0.75nlog2n. In this study, we analyze the basic topological properties of LS. We prove that LSn is a symmetrical connected graph and analyzed its subgraph characteristics. Then, we propose a routing algorithm and derive the diameter and network cost. Finally, the network costs of the LS and star graph-like networks are compared.

An optimal broadcasting algorithm without message redundancy in star graphs

1995 ◽  
Vol 6 (6) ◽  
pp. 653-658 ◽  
Author(s):  
Jang-Ping Sheu ◽  
Chao-Tsung Wu ◽  
Tzung-Shi Chen
Keyword(s):  
Star Graphs ◽  
Broadcasting Algorithm

ANALYSIS OF A CLASS OF NETWORKS BASED ON CUBIC STAR GRAPHS

1994 ◽  
Vol 04 (02) ◽  
pp. 191-222
Author(s):  
S.V.R. MADABHUSHI ◽  
S. LAKSHMIVARAHAN ◽  
S.K. DHALL
Keyword(s):  
Interconnection Networks ◽  
Fault Tolerant ◽  
Cayley Graphs ◽  
Binary Trees ◽  
Star Graph ◽  
Cubic Graphs ◽  
Topological Properties ◽  
Star Graphs ◽  
New Class ◽  
Edge Transitive

A new class of interconnection networks based on a family of graphs, called cubic graphs are introduced. These latter graphs arise as Cayley graphs of certain subgroups of the symmetric group. It turns out that these Cayley graphs are a hybrid between the binary hypercube and the star graph, and hence are called cubic star graphs, and are denoted by CS(m, n), m≥1 and n≥1. CS(m, n) inherits several of the properties of the hypercube and the star graph. In this paper, we present an analysis of the symmetric and topological properties. In particular, it is shown that CS(m, n) is edge transitive and hence maximally fault tolerant. We give an algorithm for finding the shortest path and provide an enumeration of the node disjoint paths. Optimal algorithms for single source and all-source broadcasting (also called gossiping) are derived. It is shown that CS(m, n) is Hamiltonian and interesting embeddings of several cycles, grids, and binary trees are derived. The paper concludes with a comparison of CS(m, n) with the binary hypercube and the star graph.

Sign in / Sign up

Export Citation Format

Share Document