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Fault Hamiltonicity and fault Hamiltonian connectivity of the (n, k)star graphs
 NETWORKS
, 2003
"... In this paper, we consider the fault Hamiltonicity, and the fault Hamiltonian connectivity of the (n, k)star graph Sn,k. Assume that F V(Sn,k) E(Sn,k). For n k ≥ 2, we prove that Sn,k F is Hamiltonian if F ≤ n 3 and Sn,k F is Hamiltonian connected if F ≤ n 4. For n k 1, Sn,n1 is isomo ..."
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In this paper, we consider the fault Hamiltonicity, and the fault Hamiltonian connectivity of the (n, k)star graph Sn,k. Assume that F V(Sn,k) E(Sn,k). For n k ≥ 2, we prove that Sn,k F is Hamiltonian if F ≤ n 3 and Sn,k F is Hamiltonian connected if F ≤ n 4. For n k 1, Sn,n1 is isomorphic to the nstar graph Sn which is known to be Hamiltonian if and only if n> 2 and Hamiltonian connected if and only if n 2. Moreover, all the
Designing Reliable Architecture for Stateful Fault Tolerance
 In Proceedings of Seventh International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT’06
, 2006
"... Performance and fault tolerance are two major issues that need to be addressed while designing highly available and reliable systems. The network topology or the notion of connectedness among the network nodes defines the system communication architecture and is an important design consideration for ..."
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Cited by 1 (1 self)
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Performance and fault tolerance are two major issues that need to be addressed while designing highly available and reliable systems. The network topology or the notion of connectedness among the network nodes defines the system communication architecture and is an important design consideration for fault tolerant systems. A number of fault tolerant designs for specific multiprocessor architecture exists in the literature, but none of them discriminates between stateless and stateful failover. In this paper, we propose a reliable network topology and a high availability framework which is tolerant upto a maximum of k node faults in a network and is designed specifically to meet the needs of stateful failover. Assuming the nodes in the network are capable of handling multiple processes, through our design we have been able to prove that in the event of k node failures the load can be uniformly distributed across the network ensuring load balance. We also provide an useful characterization for the network, which under the proposed framework ensures one hop communication between the required nodes.
Construction for Strongly kHamiltonian Graphs
 PROC. OF THE 19TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... The kHamiltonian graphs have been studied by many researchers. In this paper, we introduce strongly kHamiltonian graphs. A strongly kHamiltonian graph is also kHamiltonian. Moreover, we present two construction schemes for strongly kHamiltonian graphs including (k +2)join and Cartesian product ..."
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Cited by 1 (0 self)
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The kHamiltonian graphs have been studied by many researchers. In this paper, we introduce strongly kHamiltonian graphs. A strongly kHamiltonian graph is also kHamiltonian. Moreover, we present two construction schemes for strongly kHamiltonian graphs including (k +2)join and Cartesian product with K2. Applying these schemes, we can construct many new strongly kHamiltonian graphs.
Intersecting longest paths and longest cycles: A survey
 ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS 1 (1) (2013), 56–76
, 2013
"... This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention. Graphs embeddable in the cubic lattice of arbitrary dimensio ..."
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Cited by 1 (0 self)
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This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention. Graphs embeddable in the cubic lattice of arbitrary dimension, and graphs embeddable in the triangular or hexagonal lattice of the plane are also discussed. Results concerning the case when not all, but just some longest paths or cycles are intersected, for example two or three of them, are also reported.
Under the guidance of
, 2014
"... ii M.Tech. (Distributed and Mobile Computing) course affiliated to ..."
EDGE, VERTEX AND MIXED FAULTDIAMETERS
, 2008
"... Let DE q (G) denote the diameter of a graph G after deleting any of its q edges, and DV p (G) denote the diameter of G after deleting any of its p vertices. We prove that DE a (G) ≤ DV a (G) + 1 for all meaningful a. We also define mixed fault diameter DM (p,q)(G), where p vertices and q edges are ..."
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Let DE q (G) denote the diameter of a graph G after deleting any of its q edges, and DV p (G) denote the diameter of G after deleting any of its p vertices. We prove that DE a (G) ≤ DV a (G) + 1 for all meaningful a. We also define mixed fault diameter DM (p,q)(G), where p vertices and q edges are deleted at the same time. We prove that for 0 < l ≤ a, DE a (G) ≤ DM (a−ℓ,ℓ)(G) ≤ DV a (G) + 1, and give some examples.
A Distributed Algorithm of Fault Recovery For Stateful Failover
"... In [8], a high availability framework based on Harary graph as network topology has been proposed for stateful failover. Framework proposed therein exhibits an interesting property that an uniform load can be given to each nonfaulty node while maintaining fault tolerance. A challenging problem in ..."
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In [8], a high availability framework based on Harary graph as network topology has been proposed for stateful failover. Framework proposed therein exhibits an interesting property that an uniform load can be given to each nonfaulty node while maintaining fault tolerance. A challenging problem in this context, which has not been addressed in [8] is to be able to come up with a distributed algorithm of automated fault recovery which can exploit the properties exhibited by the framework. In this work, we propose a distributed algorithm with low message and round complexity for automated fault recovery in case of stateful failover. We then prove the correctness of the algorithm using techniques from formal verification. The safety, liveness and the timeliness properties of the algorithm have been verified by the model checker SPIN.
Finding Hamiltonian Cycle on Cartesian Product of a Hypotraceable Graph and a Hamiltonian Graph
 THE 25TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
, 2008
"... The interconnected network is usually represented by a graph where the vertices represent processors and the edges represent links between processors. A hypotraceable graph G is a graph with no Hamiltonian path, and for any vertex v ∈ V ( G) G−v has a Hamiltonian path. This paper investigates the Ca ..."
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The interconnected network is usually represented by a graph where the vertices represent processors and the edges represent links between processors. A hypotraceable graph G is a graph with no Hamiltonian path, and for any vertex v ∈ V ( G) G−v has a Hamiltonian path. This paper investigates the Cartesian product of a hypotraceable graph with a cycle Cn. It is shown that the Cartesian product of a hypotraceable graph and a Hamiltonian graph is Hamiltonian.