Spider web networks: a family of optimal, fault tolerant, hamiltonian bipartite graphs

Kao, Shin-Shin; Hsu, Lih‐Hsing

doi:10.1016/j.amc.2003.06.005

Cited by 20 publications

(6 citation statements)

References 7 publications

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“…SW(m,n) is a graph with the node set {(i,j)| 0 ≤ i < m, 0 ≤ j < n } , where m and n are ≥ 4, even integers such that (i,j) and (k,l) are adjacent if they satisfy one of the following conditions: (1) i=k and j=l±1; (2) j=l and k=i+1(mod m) (also presented as k=[i+1] m ) if i+j is odd or j=n-1; (3) j=l, k=i-1(mod m) if i+j is even or j=0. SW(m,n) is proved to be 1-edge Hamiltonian and 1 p -Hamiltonian [4]. Thus, the faulttolerance engaged in the bipartite Spider-Web network is systematically based.…”

Section: Mathematical Preliminariesmentioning

confidence: 94%

Securing Exposition with Parallelism in Spider-Web Networks

Hsu

2012

2012 International Symposium on Computer, Consumer and Control

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Providing well exhibition spaces is essential for promoting place economy and human welfare. After the 9-11 event, awareness of the need for antiterrorism in large-scale exhibition spaces has grown. Exhibition spaces generally have a linear route for easy identification and access control for the whole area or for individual districts. Considering on such security, wayfinding feature, regular degree-three Spider-Web networks, or SW(m,n), are prototyped as identity-oriented, dual-surveillance based networks fitted along the paths of travelers to enhance security and to sustain development. Moreover, reliable supervisory communication in the wireless area or application of radio frequency identification (RFID) is systematically communicated to counter the effects of an a d v e r s a r y ' s mu l t i path radio. For any pair of bipartite nodes,spider-web networks are assumed to offer at least two mutually independent Hamiltonian paths. Their sequential-order, connectivity, and reliability in integrative area management provides the benefits of safety/security, efficient maintenance, environmental control, and human-care image due to their effective dual sensing, fault-tolerance and hamiltonian laceability.

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Section: Mathematical Preliminariesmentioning

confidence: 94%

Securing Exposition with Parallelism in Spider-Web Networks

Hsu

2012

2012 International Symposium on Computer, Consumer and Control

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“…For many years, fault-tolerant hamiltonicity and its related issues have been widely studied in interconnection networks and for special graphs (see [1,4,5,8,10,17], Chapters 11-13 in [3], and the references therein).…”

Section: On the 1-fault Hamiltonicity For Graphs Satisfying Ore's Thementioning

confidence: 99%

On the 1-fault hamiltonicity for graphs satisfying Ore's theorem and its generalization

Shih

Kao

2014

International Journal of Computer Mathematics

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Consider any undirected and simple graph G = (V , E), where V and E denote the vertex set and the edge set of G, respectively. Let |G| = |V | = n. The well-known Ore's theorem states that if deg G (u) + deg G (v) ≥ n + k holds for each pair of nonadjacent vertices u and v of G, then G is traceable for k = −1, hamiltonian for k = 0, and hamiltonian-connected for k = 1. Lin et al. generalized Ore's theorem and showed that under the same condition as above, G is r * -connected for 1 ≤ r ≤ k + 2 with k ≥ 1. In this paper, we improve both theorems by showing that the hamiltonicity or r * -connectivity of any graph G satisfying the condition deg G (u) + deg G (v) ≥ n + k with k ≥ −1 is preserved even after one vertex or one edge is removed, unless G belongs to two exceptional families.

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“…Thus, the fault-tolerance in which we are engaged is systematically based. Moreover, GHT(m, n, 0), GHT(m, n, n/2), and SW(m, n) are Hamiltonian laceable if m, n ≥ 4 integers [16,17].…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Ubiquitous Integrity via Network Integration and Parallelism—Sustaining Pedestrian/Bike Urbanism

Hsu

2013

Algorithms

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Nowadays, due to the concern regarding environmental issues, establishing pedestrian/bike friendly urbanism is widely encouraged. To promote safety-assured, mobile communication environments, efficient, reliable maintenance, and information integrity need to be designed, especially in highly possibly interfered places. For busy traffic areas, regular degree-3 dedicated short range communication (DSRC) networks are safety and information featured with availability, reliability, and maintainability in paths of multi-lanes. For sparsely populated areas, probes of wireless sensors are rational, especially if sensor nodes can be organized to enhance security, reliability, and flexibility. Applying alternative network topologies, such as spider-webs, generalized honeycomb tori, and cube-connected cycles, for comparing and analyzing is proposed in DSRC and cellular communications to enhance integrity in communications.

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Spider web networks: a family of optimal, fault tolerant, hamiltonian bipartite graphs

Cited by 20 publications

References 7 publications

Securing Exposition with Parallelism in Spider-Web Networks

Securing Exposition with Parallelism in Spider-Web Networks

On the 1-fault hamiltonicity for graphs satisfying Ore's theorem and its generalization

Ubiquitous Integrity via Network Integration and Parallelism—Sustaining Pedestrian/Bike Urbanism

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