Parallel Construction of Independent Spanning Trees on Enhanced Hypercubes

Yang, Jinn‐Shyong; Chang, Jou–Ming; Pai, Kung-Jui; Chan, Hung-Chang

doi:10.1109/tpds.2014.2367498

Cited by 41 publications

(16 citation statements)

References 28 publications

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“…Zehavi and Itai [9] proposed the following conjecture: If G is a k-connected graph and r∈V(G) is an arbitrary vertex, then G admits k ISTs rooted at r. From then on, the conjecture has been confirmed only for k≤4 and is still open for k≥5. Also, by providing construction schemes of ISTs, the conjecture is affirmative for some restricted classes of graphs (e.g., see recent papers [10,11] and the references quoted therein). We now give the following property (here we omit the proof).…”

Section: The Heights Of Independent Spanning Treesmentioning

confidence: 94%

Computing the Wide Diameter of Regular Hyper-Star Networks Using Independent Spanning Trees

Chang¹

2017

dtcse

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Abstract. In this paper, we determine the wide diameter of a regular hyper-star network HS (2k,k). We first provide a connection between the wide diameter and the maximum height of a set of particular spanning trees, called independent spanning trees (ISTs for short), of a network. According to this relation, we analyze the height of a set of constructed ISTs in HS (2k,k) to establish an upper bound of the wide diameter of HS(2k,k). By contrast, we take the known result of fault diameter of HS (2k,k) as a lower bound. As a consequence, we obtain the following result: D w (HS(2k,k))=2k+1 for k≥2, where D w (G) stands for the wide diameter of a graph G.

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Section: The Heights Of Independent Spanning Treesmentioning

confidence: 94%

Computing the Wide Diameter of Regular Hyper-Star Networks Using Independent Spanning Trees

Chang¹

2017

dtcse

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“…As a variant of the , enhanced hypercubes (n ≥2, (1≤k ≤ n−1) are proposed to improve the efficiency of the hypercube architecture and have found substantial applications. Inherited from , is also a regular graph [15], [20]. But the enhanced hypercubes are much more attractive than normal hypercubes due to its potential nice topological properties.…”

Section: Enhanced Hypercube Networkmentioning

confidence: 99%

“…The edges of in are hypercube edges and the remaining edges of are called complementary edges [4], [7], [8], [9], [16], [17], [18], [20], [21].When k=0, reduces to the n-dimensional hypercube. The enhanced hypercubes (1≤ k ≤ n−1) proposed by Tzeng and Wei [15] are (n +1) regular.…”

Section: Enhanced Hypercube Networkmentioning

confidence: 99%

Induced H-Packing k-Partition Problem in Certain Networks

Theresal¹,

Xavier²,

Raja³

2019

IJRTE

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A collection = {H1 ,H2 ,..., Hr } of induced sub graphs of a graph G is said to be sg-independent if (i) V(Hi ) V(Hj )= , i j, 1≤ i, j≤ r and (ii) no edge of G has its one end in Hi and the other end in Hj , i j, 1≤ i, j≤ r. If Hi H, ∀ i, 1≤ i ≤r, then is referred to as a H-independent set of G. Let be a perfect or almost perfect H-packing of a graph G. Finding a partition of such that is Hindependent set, ∀ i, 1 ≤ i ≤ k, with minimum k is called the induced H-packing kpartition problem of G. The induced H-packing k-partition number denoted by ipp(G,H) is defined as ipp(G,H) = min (G,H) where the minimum is taken over all H-packing of G. In this paper we obtain the induced H-packing k-partition number for Enhanced hypercube, Augmented Cubes and Crossed Cube networks where H is isomorphic to and .

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“…For instance, the construction of ISTS on some variations of hypercubes [3], [22], [32], [33], [40], torus networks [31], recursive circulant graphs [37], [38], and special subclasses of Cayley networks [7], [17], [18], [20], [21]. In particular, special topics related to IST include the research on reducing the height of ISTs [34], [36], [39] and parallel construction of ISTs [4]- [6], [35], [40], [41].…”

Section: Introductionmentioning

confidence: 99%