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Статті в журналах з теми "Spanning graphs of hypercubes"

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Автор: Grafiati

Опубліковано: 4 травня 2024

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1

Kobeissi, Mohamed, and Michel Mollard. "Disjoint cycles and spanning graphs of hypercubes." Discrete Mathematics 288, no. 1-3 (November 2004): 73–87. http://dx.doi.org/10.1016/j.disc.2004.08.005.

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2

Kobeissi, Mohamed, and Michel Mollard. "Spanning graphs of hypercubes: starlike and double starlike trees." Discrete Mathematics 244, no. 1-3 (February 2002): 231–39. http://dx.doi.org/10.1016/s0012-365x(01)00086-3.

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3

LIN, LAN, and YIXUN LIN. "The Minimum Stretch Spanning Tree Problem for Hamming Graphs and Higher-Dimensional Grids." Journal of Interconnection Networks 20, no. 01 (March 2020): 2050004. http://dx.doi.org/10.1142/s0219265920500048.

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Анотація:

The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a graph invariant σ(G), called the tree-stretch of G. The problem has been proved NP-hard. In this paper we present a general approach to determine the exact values σ(G) for a series of typical graphs arising from communication networks, such as Hamming graphs and higher-dimensional grids (including hypercubes).

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4

RIORDAN, OLIVER. "Spanning Subgraphs of Random Graphs." Combinatorics, Probability and Computing 9, no. 2 (March 2000): 125–48. http://dx.doi.org/10.1017/s0963548399004150.

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Let Gp be a random graph on 2d vertices where edges are selected independently with a fixed probability p > ¼, and let H be the d-dimensional hypercube Qd. We answer a question of Bollobás by showing that, as d → ∞, Gp almost surely has a spanning subgraph isomorphic to H. In fact we prove a stronger result which implies that the number of d-cubes in G ∈ [Gscr ](n, M) is asymptotically normally distributed for M in a certain range. The result proved can be applied to many other graphs, also improving previous results for the lattice, that is, the 2-dimensional square grid. The proof uses the second moment method – writing X for the number of subgraphs of G isomorphic to H, where G is a suitable random graph, we expand the variance of X as a sum over all subgraphs of H itself. As the subgraphs of H may be quite complicated, most of the work is in estimating the various terms of this sum.

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5

YANG, JINN-SHYONG, JOU-MING CHANG, SHYUE-MING TANG, and YUE-LI WANG. "CONSTRUCTING MULTIPLE INDEPENDENT SPANNING TREES ON RECURSIVE CIRCULANT GRAPHS G(2m, 2)." International Journal of Foundations of Computer Science 21, no. 01 (February 2010): 73–90. http://dx.doi.org/10.1142/s0129054110007143.

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A recursive circulant graph G(N,d) has N = cdm vertices labeled from 0 to N - 1, where d ⩾ 2, m ⩾ 1, and 1 ⩽ c < d, and two vertices x,y ∈ G(N,d) are adjacent if and only if there is an integer k with 0 ⩽ k ⩽ ⌈ log d N⌉ - 1 such that x ± dk ≡ y ( mod N). With the aid of recursive structure, such class of graphs has many attractive features and was considered as a topology of interconnection networks for computing systems. The design of multiple independent spanning trees (ISTs) has many applications in network communication. For instance, it is useful for fault-tolerant broadcasting and secure message distribution. In the previous work of Yang et al. (2009), we provided a constructing scheme to build k ISTs on G(cdm,d) with d ⩾ 3, where k is the connectivity of G(cdm,d). However, the proposed constructing rules cannot be applied to the case of d = 2. For the integrity of solving the IST problem on recursive circulant graphs, this paper deals with the case of G(2m,2) using a set of different constructing rules. Especially, we show that the heights of ISTs for G(2m,2) are lower than the known optimal construction of hypercubes with the same number of vertices.

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6

Tien, Jenn-Yang, and Wei-Pang Yang. "Hierarchical spanning trees and distributing on incomplete hypercubes." Parallel Computing 17, no. 12 (December 1991): 1343–60. http://dx.doi.org/10.1016/s0167-8191(05)80002-x.

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7

Pai, Kung-Jui. "Dual Protection Routing Trees on Graphs." Mathematics 11, no. 14 (July 24, 2023): 3255. http://dx.doi.org/10.3390/math11143255.

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Анотація:

In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then showed that “whether there is a protection routing to the destination” is NP-complete. Tapolcai found that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we proposed dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we proposed a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs Kn, complete bipartite graphs Km,n, hypercubes Qn, and locally twisted cubes LTQn as examples, we provided a recursive method to construct dual-PRTs on them. This article showed that there are no two CISTs on K3,3, Q3, and LTQ3, but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Qn and LTQn, we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs.

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8

Yang, Jinn-Shyong, Shyue-Ming Tang, Jou-Ming Chang, and Yue-Li Wang. "Parallel construction of optimal independent spanning trees on hypercubes." Parallel Computing 33, no. 1 (February 2007): 73–79. http://dx.doi.org/10.1016/j.parco.2006.12.001.

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9

Nieminen, Juhani, Matti Peltola, and Pasi Ruotsalainen. "On Graphs Like Hypercubes." Tsukuba Journal of Mathematics 32, no. 1 (June 2008): 37–48. http://dx.doi.org/10.21099/tkbjm/1496165191.

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10

Locke, Stephen C., and Richard Stong. "Spanning Cycles in Hypercubes: 10892." American Mathematical Monthly 110, no. 5 (May 2003): 440. http://dx.doi.org/10.2307/3647840.

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11

Duckworth, W., P. E. Dunne, A. M. Gibbons, and M. Zito. "Leafy spanning trees in hypercubes." Applied Mathematics Letters 14, no. 7 (October 2001): 801–4. http://dx.doi.org/10.1016/s0893-9659(01)00047-7.

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12

Caha, Rostislav, and Václav Koubek. "Spanning multi-paths in hypercubes." Discrete Mathematics 307, no. 16 (July 2007): 2053–66. http://dx.doi.org/10.1016/j.disc.2005.12.050.

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13

Caha, R., and V. Koubek. "Spanning Regular Caterpillars in Hypercubes." European Journal of Combinatorics 18, no. 3 (April 1997): 249–66. http://dx.doi.org/10.1006/eujc.1996.0090.

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14

Brešar, Boštjan. "Intersection graphs of maximal hypercubes." European Journal of Combinatorics 24, no. 2 (February 2003): 195–209. http://dx.doi.org/10.1016/s0195-6698(02)00142-7.

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15

Laborde, Jean Marie, and RafaïMourad Madani. "Generalized hypercubes and (0,2)-graphs." Discrete Mathematics 165-166 (March 1997): 447–59. http://dx.doi.org/10.1016/s0012-365x(96)00343-3.

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16

Ma, Meijie. "The spanning connectivity of folded hypercubes☆." Information Sciences 180, no. 17 (September 1, 2010): 3373–79. http://dx.doi.org/10.1016/j.ins.2010.05.015.

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17

Fink, Jiří. "Matching graphs of Hypercubes and Complete Bipartite Graphs." Electronic Notes in Discrete Mathematics 29 (August 2007): 345–51. http://dx.doi.org/10.1016/j.endm.2007.07.059.

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18

Fink, Jiří. "Matching graphs of hypercubes and complete bipartite graphs." European Journal of Combinatorics 30, no. 7 (October 2009): 1624–29. http://dx.doi.org/10.1016/j.ejc.2009.03.007.

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19

LI, QIULI, and WANTAO NING. "Matching Preclusion for Exchanged Hypercubes." Journal of Interconnection Networks 19, no. 03 (September 2019): 1940008. http://dx.doi.org/10.1142/s0219265919400085.

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Анотація:

As spanning subgraphs of hypercubes, exchanged hypercubes contain less edges but maintain lots of desired properties of hypercubes. This paper considers matching preclusion, a kind of measures of edge-fault tolerance, of exchanged hypercubes EH(s, t). We show that EH(s, t) is maximally matched, that is, for s ≥ t, mp(EH(s, t)) = t + 1 and EH(s, t) is super matched if and only if (s, t) ≠ (1, 1). Comparing with results of matching preclusion for hypercubes, we conclude that exchanged hypercubes maintain the matching preclusion property of hypercubes, except for EH(1, 1).

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20

Al-Ezeh, Hasan, Omar A. AbuGheim, and Eman A. AbuHijleh. "Characterizing which powers of hypercubes and folded hypercubes are divisor graphs." Discussiones Mathematicae Graph Theory 35, no. 2 (2015): 301. http://dx.doi.org/10.7151/dmgt.1801.

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21

Andreae, Thomas, and Martin Hintz. "On Hypercubes in de Bruijn Graphs." Parallel Processing Letters 08, no. 02 (June 1998): 259–68. http://dx.doi.org/10.1142/s0129626498000274.

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Анотація:

We prove that the hypercube of odd dimension 2k + 1 is a subgraph of the de Bruijn graph of alphabet size d and diameter 2 if and only if d ≥ 3 · 2k-1. This complements previous results of Heydemann, Opatrny, and Sotteau (1994) and Andreae et al. (1995), thus yielding a complete solution of the problem of determining, for all integers m, n ≥ 2, the least number d = d(m, n) for which the hypercube of dimension m is a subgraph of the de Bruijn graph of alphabet size d and diameter n.

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22

Nieminen, J., and M. Peltola. "A generalization of hypercubes: Complemented graphs." Applied Mathematics Letters 12, no. 4 (May 1999): 89–94. http://dx.doi.org/10.1016/s0893-9659(99)00040-3.

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23

Klugerman, Michael, Alexander Russell, and Ravi Sundaram. "On embedding complete graphs into hypercubes." Discrete Mathematics 186, no. 1-3 (May 1998): 289–93. http://dx.doi.org/10.1016/s0012-365x(97)00239-2.

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24

Chung, Yeh-Ching, and Sanjay Ranka. "Mapping finite element graphs on hypercubes." Journal of Supercomputing 6, no. 3-4 (December 1992): 257–82. http://dx.doi.org/10.1007/bf00155802.

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25

Deza, M., and M. I. Shtogrin. "Embeddings of chemical graphs in hypercubes." Mathematical Notes 68, no. 3 (September 2000): 295–305. http://dx.doi.org/10.1007/bf02674552.

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26

Mane, S. A., and B. N. Waphare. "Regular connected bipancyclic spanning subgraphs of hypercubes." Computers & Mathematics with Applications 62, no. 9 (November 2011): 3551–54. http://dx.doi.org/10.1016/j.camwa.2011.08.071.

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27

Barden, Benjamin, Ran Libeskind-Hadas, Janet Davis, and William Williams. "On edge-disjoint spanning trees in hypercubes." Information Processing Letters 70, no. 1 (April 1999): 13–16. http://dx.doi.org/10.1016/s0020-0190(99)00033-2.

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28

Sonawane, A. V., and Y. M. Borse. "Decomposing hypercubes into regular connected subgraphs." Discrete Mathematics, Algorithms and Applications 08, no. 04 (November 8, 2016): 1650065. http://dx.doi.org/10.1142/s1793830916500658.

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Анотація:

It is known that the [Formula: see text]-dimensional hypercube [Formula: see text] for [Formula: see text] with [Formula: see text] can be decomposed into two spanning bipancyclic subgraphs [Formula: see text] and [Formula: see text] such that [Formula: see text] is [Formula: see text]-regular and [Formula: see text]-connected for [Formula: see text] In this paper, we prove that if [Formula: see text] with [Formula: see text] and at most one [Formula: see text] odd, then [Formula: see text] can be decomposed into [Formula: see text] spanning subgraphs [Formula: see text], [Formula: see text] such that [Formula: see text] is [Formula: see text]-regular and [Formula: see text]-connected for [Formula: see text]

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29

Najjar, Walid, and Pradip K. Srimani. "Conditional Disconnection Probability in Star Graphs." VLSI Design 1, no. 1 (January 1, 1993): 61–70. http://dx.doi.org/10.1155/1993/84924.

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Анотація:

Recently a new interconnection topology has been proposed which compares very favorably with the well known n-cubes (hypercubes) in terms of degree, diameter, fault-tolerance and applicability in VLSI design. In this paper we use a new probabilistic measure of network fault tolerance expressed as the probability of disconnection to study the robustness of star graphs. We derive analytical approximation for the disconnection probability of star graphs and verify it with Monte Carlo simulation. We then compare the results with hypercubes [4]. We also use the measures of network resilience and relative network resilience to evaluate the effects of the disconnection probability on the reliability of star graphs.

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30

Borse, Y. M., and S. A. Kandekar. "Decomposition of hypercubes into regular connected bipancyclic subgraphs." Discrete Mathematics, Algorithms and Applications 07, no. 03 (September 2015): 1550033. http://dx.doi.org/10.1142/s1793830915500330.

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Анотація:

In this paper, we consider the problem of decomposing the edge set of the hypercube Qn into two spanning, regular, connected, bipancyclic subgraphs. We prove that if n = n1 + n2 with n1 ≥ 2 and n2 ≥ 2, then the edge set of Qn can be decomposed into two spanning, bipancyclic subgraphs H1 and H2 such that Hi is ni-regular and ni-connected for i = 1, 2.

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31

Berrachedi, A., and M. Mollard. "Median graphs and hypercubes, some new characterizations." Discrete Mathematics 208-209 (October 1999): 71–75. http://dx.doi.org/10.1016/s0012-365x(99)00063-1.

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32

Matsubayashi, Akira, and Shuichi Ueno. "Small congestion embedding of graphs into hypercubes." Networks 33, no. 1 (January 1999): 71–77. http://dx.doi.org/10.1002/(sici)1097-0037(199901)33:1<71::aid-net5>3.0.co;2-3.

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33

Shpectorov, S. V. "On Scale Embeddings of Graphs into Hypercubes." European Journal of Combinatorics 14, no. 2 (March 1993): 117–30. http://dx.doi.org/10.1006/eujc.1993.1016.

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34

BEST, ANA, MARKUS KLIEGL, SHAWN MEAD-GLUCHACKI, and CHRISTINO TAMON. "MIXING OF QUANTUM WALKS ON GENERALIZED HYPERCUBES." International Journal of Quantum Information 06, no. 06 (December 2008): 1135–48. http://dx.doi.org/10.1142/s0219749908004377.

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Анотація:

We study continuous-time quantum walks on graphs which generalize the hypercube. The only known family of graphs whose quantum walk instantaneously mixes to uniform is the Hamming graphs with small arities. We show that quantum uniform mixing on the hypercube is robust under the addition of perfect matchings but not much else. Our specific results include: • The graph obtained by augmenting the hypercube with an additive matching x ↦ x ⊕ η is instantaneous uniform mixing whenever |η| is even, but with a slower mixing time. This strictly includes the result of Moore and Russell1 on the hypercube. • The class of Hamming graphs H(n,q) is not uniform mixing if and only if q ≥ 5. This is a tight characterization of quantum uniform mixing on Hamming graphs; previously, only the status of H(n,q) with q < 5 was known. • The bunkbed graph [Formula: see text] whose adjacency matrix is I ⊗ Qn + X ⊗ Af, where Af is a [Formula: see text]-circulant matrix defined by a Boolean function f, is not uniform mixing if the Fourier transform of f has support of size smaller than 2n-1. This explains why the hypercube is uniform mixing and why the join of two hypercubes is not. Our work exploits the rich spectral structure of the generalized hypercubes and relies heavily on Fourier analysis of group-circulants.

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35

Chang, Chung-Hao, Cheng-Kuan Lin, Jimmy J. M. Tan, Hua-Min Huang, and Lih-Hsing Hsu. "The super spanning connectivity and super spanning laceability of the enhanced hypercubes." Journal of Supercomputing 48, no. 1 (April 18, 2008): 66–87. http://dx.doi.org/10.1007/s11227-008-0206-0.

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36

Gu, Mei-Mei, Rong-Xia Hao, and Eddie Cheng. "Note on Applications of Linearly Many Faults." Computer Journal 63, no. 9 (November 15, 2019): 1406–16. http://dx.doi.org/10.1093/comjnl/bxz088.

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Анотація:

Abstract Most graphs have this property: after removing a linear number of vertices from a graph, the surviving graph is either connected or consists of a large connected component and small components containing a small number of vertices. This property can be applied to derive fault-tolerance related network parameters: extra edge connectivity and component edge connectivity. Using this general property, we obtained the $h$-extra edge connectivity and $(h+2)$-component edge connectivity of augmented cubes, Cayley graphs generated by transposition trees, complete cubic networks (including hierarchical cubic networks), generalized exchanged hypercubes (including exchanged hypercubes) and dual-cube-like graphs (including dual cubes).

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37

Arulanand, S., R. Sundara Rajan, and S. Prabhu. "2-domination number for special classes of hypercubes, enhanced hypercubes and Knödel graphs." International Journal of Networking and Virtual Organisations 29, no. 2 (2023): 168–82. http://dx.doi.org/10.1504/ijnvo.2023.134993.

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38

AbuGhneim, Omar A., Hasan Al-Ezeh, and Mahmoud Al-Ezeh. "The Wiener Polynomial of thekthPower Graph." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–6. http://dx.doi.org/10.1155/2007/24873.

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Анотація:

We presented a formula for the Wiener polynomial of thekthpower graph. We use this formula to find the Wiener polynomials of thekthpower graphs of paths, cycles, ladder graphs, and hypercubes. Also, we compute the Wiener indices of these graphs.

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39

Das, Sajal K., Narsingh Deo, and Sushil Prasad. "Two minimum spanning forest algorithms on fixed-size hypercube computers." Parallel Computing 15, no. 1-3 (September 1990): 179–87. http://dx.doi.org/10.1016/0167-8191(90)90041-7.

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40

Gledel, Valentin, and Vesna Iršič. "Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 3 (September 17, 2019): 2757–67. http://dx.doi.org/10.1007/s40840-019-00833-6.

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41

GU, QIAN-PING, and SHIETUNG PENG. "FAULT TOLERANT ROUTING IN HYPERCUBES AND STAR GRAPHS." Parallel Processing Letters 06, no. 01 (March 1996): 127–36. http://dx.doi.org/10.1142/s0129626496000133.

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Анотація:

In this paper, we give two linear time algorithms for node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn and star graphs Gn. The first algorithm, given at most n−1 arbitrary fault nodes and two non-fault nodes s and t in Hn, finds a fault-free path s→t of length at most [Formula: see text] in O(n) time, where d(s, t) is the distance between s and t. Our second algorithm, given at most n−2 fault nodes and two non-fault nodes s and t in Gn, finds a fault-free path s→t of length at most d(Gn)+3 in O(n) time, where [Formula: see text] is the diameter of Gn. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

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42

Graham, Niall, and Frank Harary. "Hypercubes, shuffle-exchange graphs and de Bruijn digraphs." Mathematical and Computer Modelling 17, no. 11 (June 1993): 69–74. http://dx.doi.org/10.1016/0895-7177(93)90255-w.

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43

Bruck, J., R. Cypher, and D. Soroker. "Embedding cube-connected cycles graphs into faulty hypercubes." IEEE Transactions on Computers 43, no. 10 (1994): 1210–20. http://dx.doi.org/10.1109/12.324546.

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44

Lobov, A. A., and M. B. Abrosimov. "Vertex extensions of 4-layer graphs and hypercubes." Izvestiya of Saratov University. Mathematics. Mechanics. Informatics 22, no. 4 (November 23, 2022): 536–48. http://dx.doi.org/10.18500/1816-9791-2022-22-4-536-548.

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45

Aïder, Méziane, Sylvain Gravier, and Kahina Meslem. "Isometric embeddings of subdivided connected graphs into hypercubes." Discrete Mathematics 309, no. 22 (November 2009): 6402–7. http://dx.doi.org/10.1016/j.disc.2008.10.030.

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46

Lee, Shyi-Long, and Yeong-Nan Yeh. "Topological analysis of some special of graphs. Hypercubes." Chemical Physics Letters 171, no. 4 (August 1990): 385–88. http://dx.doi.org/10.1016/0009-2614(90)85383-n.

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47

YANG, Yi-Xian, Kung-Jui PAI, Ruay-Shiung CHANG, and Jou-Ming CHANG. "Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes." IEICE Transactions on Information and Systems E102.D, no. 12 (December 1, 2019): 2409–12. http://dx.doi.org/10.1587/transinf.2019pal0001.

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