Fractional Matching Preclusion for Folded Petersen Cube Networks

2020 ◽  
Vol 20 (04) ◽  
pp. 2150003
Author(s):  
JINYU ZOU ◽  
CHENGFU YE ◽  
HAIZHEN REN

Let F be an edge set and F′ a subset of edges and/or vertices of a graph G. Then F is a fractional matching preclusion(FMP) set (F′ is a fractional strong matching preclusion (FSMP) set) if G − F (G − F′) does not contain fractional perfect matching. The FMP(FSMP) number of G is the minimum size of FMP(FSMP) sets of G. The concept of matching preclusion was introduced by Brigham et al., as a measure of robustness in the event of edge failure in interconnection networks. An interconnection network of a larger MP number may be considered as more robust in the event of link failures. The problem of fractional matching preclusion is a generalization of matching preclusion. In this paper, we obtain the FMP and FSMP number for the folded Petersen cube networks. All the optimal fractional strong matching preclusion sets of these graphs are categorized.

2021 ◽  
Vol 31 (01) ◽  
pp. 2150001
Author(s):  
He Zhang ◽  
Jinyu Zou ◽  
Shuangshuang Zhang ◽  
Chengfu Ye

Let [Formula: see text] be a set edges and [Formula: see text] be a set of edges and/or vertices of a graph [Formula: see text], then [Formula: see text] (resp. [Formula: see text]) is a fractional matching preclusion set (resp. fractional strong matching preclusion set) if [Formula: see text] (resp. [Formula: see text]) contains no fractional perfect matching. The fractional matching preclusion number (resp. fractional strong matching preclusion number) of [Formula: see text] is the minimum size of fractional matching preclusion set (resp. fractional strong matching preclusion set) of [Formula: see text]. In this paper, we obtain the fractional matching preclusion number and fractional strong matching preclusion number of the DHcube [Formula: see text] for [Formula: see text]. In addition, all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.


2019 ◽  
Vol 19 (03) ◽  
pp. 1940010
Author(s):  
HUAZHONG LÜ ◽  
TINGZENG WU

The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, which extend some known results.


2021 ◽  
Author(s):  
Karthik K ◽  
Sudarson Jena ◽  
Venu Gopal T

Abstract A Multiprocessor is a system with at least two processing units sharing access to memory. The principle goal of utilizing a multiprocessor is to process the undertakings all the while and support the system’s performance. An Interconnection Network interfaces the various handling units and enormously impacts the exhibition of the whole framework. Interconnection Networks, also known as Multi-stage Interconnection Networks, are node-to-node links in which each node may be a single processor or a group of processors. These links transfer information from one processor to the next or from the processor to the memory, allowing the task to be isolated and measured equally. Hypercube systems are a kind of system geography used to interconnect various processors with memory modules and precisely course the information. Hypercube systems comprise of 2n nodes. Any Hypercube can be thought of as a graph with nodes and edges, where a node represents a processing unit and an edge represents a connection between the processors to transmit. Degree, Speed, Node coverage, Connectivity, Diameter, Reliability, Packet loss, Network cost, and so on are some of the different system scales that can be used to measure the performance of Interconnection Networks. A portion of the variations of Hypercube Interconnection Networks include Hypercube Network, Folded Hypercube Network, Multiple Reduced Hypercube Network, Multiply Twisted Cube, Recursive Circulant, Exchanged Crossed Cube Network, Half Hypercube Network, and so forth. This work assesses the performing capability of different variations of Hypercube Interconnection Networks. A group of properties is recognized and a weight metric is structured utilizing the distinguished properties to assess the performance exhibition. Utilizing this weight metric, the performance of considered variations of Hypercube Interconnection Networks is evaluated and summed up to recognize the effective variant. A compact survey of a portion of the variations of Hypercube systems, geographies, execution measurements, and assessment of the presentation are examined in this paper. Degree and Diameter are considered to ascertain the Network cost. On the off chance that Network Cost is considered as the measurement to assess the exhibition, Multiple Reduced Hypercube stands ideal with its lower cost. Notwithstanding it, on the off chance that we think about some other properties/ scales/metrics to assess the performance, any variant other than MRH may show considerably more ideal execution. The considered properties probably won't be ideally adequate to assess the effective performance of Hypercube variations in all respects. On the off chance that a sensibly decent number of properties are utilized to assess the presentation, a proficient variation of Hypercube Interconnection Network can be distinguished for a wide scope of uses. This is the inspiration to do this research work.


2002 ◽  
Vol 03 (01n02) ◽  
pp. 49-65 ◽  
Author(s):  
NADER F. MIR

A thorough routing analysis of a switching network called the spherical switching network for high-speed applications is presented in this paper. The spherical switching network has a cyclic, regular, and highly expandable structure with a simple self-routing scheme. The network is constructed with fixed-size switch elements regardless of the size of the network. Each switch element consists of a carefully-selected sized 9 input/output crossbar and a local controller. One of the nine pairs of links is external and carries the external traffic, and the other eight pairs are internal. The contention resolution in each switch element is based on deflection of losing packets and incremental priority of packets. The switch elements do not utilize any buffering within the network. The analysis shows that this network clearly outperforms typical interconnection networks currently being deployed in practical switches and routers such as Banyan network. In order to keep the number of deflections low, each incoming external link is connected to a buffer with flow control capabilities. Due to the special arrangement of interconnections in the network, a much larger number of shortest paths between each pair of source/destination exists. The related analysis for finding the number of hops and shortest paths appear in this paper.


2018 ◽  
Vol 29 (06) ◽  
pp. 995-1001 ◽  
Author(s):  
Shuli Zhao ◽  
Weihua Yang ◽  
Shurong Zhang ◽  
Liqiong Xu

Fault tolerance is an important issue in interconnection networks, and the traditional edge connectivity is an important measure to evaluate the robustness of an interconnection network. The component edge connectivity is a generalization of the traditional edge connectivity. The [Formula: see text]-component edge connectivity [Formula: see text] of a non-complete graph [Formula: see text] is the minimum number of edges whose deletion results in a graph with at least [Formula: see text] components. Let [Formula: see text] be an integer and [Formula: see text] be the decomposition of [Formula: see text] such that [Formula: see text] and [Formula: see text] for [Formula: see text]. In this note, we determine the [Formula: see text]-component edge connectivity of the hypercube [Formula: see text], [Formula: see text] for [Formula: see text]. Moreover, we classify the corresponding optimal solutions.


1998 ◽  
Vol 09 (01) ◽  
pp. 25-37 ◽  
Author(s):  
THOMAS J. CORTINA ◽  
ZHIWEI XU

We present a family of interconnection networks named the Cube-Of-Rings (COR) networks along with their basic graph-theoretic properties. Aspects of group graph theory are used to show the COR networks are symmetric and optimally fault tolerant. We present a closed-form expression of the diameter and optimal one-to-one routing algorithm for any member of the COR family. We also discuss the suitability of the COR networks as the interconnection network of scalable parallel computers.


2020 ◽  
Vol 20 (03) ◽  
pp. 2050011
Author(s):  
JUTAO ZHAO ◽  
SHIYING WANG

The connectivity and diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and interconnection network has a underlying topology, which usually presented by a graph. As a famous topology structure of interconnection networks, the n-dimensional leaf-sort graph CFn has many good properties. In this paper, we prove that (a) the restricted edge connectivity of CFn (n ≥ 3) is 3n − 5 for odd n and 3n − 6 for even n; (b) CFn (n ≥ 5) is super restricted edge-connected; (c) the nature diagnosability of CFn (n ≥ 4) under the PMC model is 3n − 4 for odd n and 3n − 5 for even n; (d) the nature diagnosability of CFn (n ≥ 5) under the MM* model is 3n − 4 for odd n and 3n − 5 for even n.


2019 ◽  
Vol 29 (03) ◽  
pp. 1950011
Author(s):  
Jiafei Liu ◽  
Shuming Zhou ◽  
Zhendong Gu ◽  
Yihong Wang ◽  
Qianru Zhou

The independent number and domination number are two essential parameters to assess the resilience of the interconnection network of multiprocessor systems which is usually modeled by a graph. The independent number, denoted by [Formula: see text], of a graph [Formula: see text] is the maximum cardinality of any subset [Formula: see text] such that no two elements in [Formula: see text] are adjacent in [Formula: see text]. The domination number, denoted by [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of any subset [Formula: see text] such that every vertex in [Formula: see text] is either in [Formula: see text] or adjacent to an element of [Formula: see text]. But so far, determining the independent number and domination number of a graph is still an NPC problem. Therefore, it is of utmost importance to determine the number of independent and domination number of some special networks with potential applications in multiprocessor system. In this paper, we firstly resolve the exact values of independent number and upper and lower bound of domination number of the [Formula: see text]-graph, a common generalization of various popular interconnection networks. Besides, as by-products, we derive the independent number and domination number of [Formula: see text]-star graph [Formula: see text], [Formula: see text]-arrangement graph [Formula: see text], as well as three special graphs.


2005 ◽  
Vol 06 (04) ◽  
pp. 361-382 ◽  
Author(s):  
K. V. Arya ◽  
R. K. Ghosh

This paper proposes a technique to modify a Multistage Interconnection Network (MIN) to augment it with fault tolerant capabilities. The augmented MIN is referred to as Enhanced MIN (E-MIN). The technique employed for construction of E-MIN is compared with the two known physical fault tolerance techniques, namely, extra staging and chaining. EMINs are found to be more generic than extra staged networks and less expensive than chained networks. The EMIN realizes all the permutations realizable by the original MIN. The routing strategies under faulty and fault free conditions are shown to be very simple in the case of E-MINs.


2009 ◽  
Vol 10 (03) ◽  
pp. 189-204 ◽  
Author(s):  
EDDIE CHENG ◽  
KE QIU ◽  
ZHIZHANG SHEN

An important and interesting parameter of an interconnection network is the number of vertices of a specific distance from a specific vertex. This is known as the surface area or the Whitney number of the second kind. In this paper, we give explicit formulas for the surface areas of the (n, k)-star graphs and the arrangement graphs via the generating function technique. As a direct consequence, these formulas will also provide such explicit formulas for the star graphs, the alternating group graphs and the split-stars since these graphs are related to the (n, k)-star graphs and the arrangement graphs. In addition, we derive the average distances for these graphs.


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