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Journal articles on the topic 'Hamiltonian graphs'

Author: Grafiati

Published: 7 September 2021

Last updated: 25 July 2025

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1

Nagarathnamma, K. G., Leena N. Shenoy, and Sowmya Krishna. "Modified Detour Index of Hamiltonian Connected (Laceable) Graphs." Indian Journal Of Science And Technology 17, no. 19 (2024): 1923–34. http://dx.doi.org/10.17485/ijst/v17i19.1033.

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Objectives: To explore the bounds for the modified detour index of certain Hamiltonian connected and laceable graphs. Methods: The Wiener index , detour index and the modified detour index are used. Findings: Here we introduce the modified detour index and its least upper bounds for Hamiltonian connected and laceable graphs, by formulating the constraints. Novelty: Based on the modified detour index, the bounds for some special graphs such as: Hamiltonian connected graphs of two families of convex polytopes ( and ) and Hamiltonian laceable graphs of spider graph ( ) and image graph of prism gr

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2

K, G. Nagarathnamma, N. Shenoy Leena, and Krishna Sowmya. "Modified Detour Index of Hamiltonian Connected (Laceable) Graphs." Indian Journal of Science and Technology 17, no. 19 (2024): 1923–34. https://doi.org/10.17485/IJST/v17i19.1033.

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Abstract <strong>Objectives:</strong> To explore the bounds for the modified detour index of certain Hamiltonian connected and laceable graphs. <strong>Methods:</strong> The Wiener index , detour index and the modified detour index are used. <strong>Findings:</strong> Here we introduce the modified detour index and its least upper bounds for Hamiltonian connected and laceable graphs, by formulating the constraints. <strong>Novelty:</strong> Based on the modified detour index, the bounds for some special graphs such as: Hamiltonian connected graphs of two fami

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3

Thirusangu, K., and K. Rangarajan. "Marked graphs and hamiltonian graphs." Microelectronics Reliability 37, no. 8 (1997): 1243–50. http://dx.doi.org/10.1016/s0026-2714(97)00001-2.

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4

Katona, D., A. Kostochka, Ya Pykh, and B. Stechkin. "Locally Hamiltonian graphs." Mathematical Notes of the Academy of Sciences of the USSR 45, no. 1 (1989): 25–29. http://dx.doi.org/10.1007/bf01158712.

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5

Chen, Ya-Chen, and Z. Füredi. "Hamiltonian Kneser Graphs." Combinatorica 22, no. 1 (2002): 147–49. http://dx.doi.org/10.1007/s004930200007.

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6

Kewen, Zhao, Hong-Jian Lai, and Ju Zhou. "Hamiltonian-connected graphs." Computers & Mathematics with Applications 55, no. 12 (2008): 2707–14. http://dx.doi.org/10.1016/j.camwa.2007.10.018.

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7

Wu, Baoyindureng, and Jixiang Meng. "Hamiltonian jump graphs." Discrete Mathematics 289, no. 1-3 (2004): 95–106. http://dx.doi.org/10.1016/j.disc.2004.09.003.

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8

Ebrahimi, Mahdi, Ali Iranmanesh, and Mohammad Ali Hosseinzadeh. "Hamiltonian character graphs." Journal of Algebra 428 (April 2015): 54–66. http://dx.doi.org/10.1016/j.jalgebra.2014.12.038.

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9

Harary, Frank, and Uri Peled. "Hamiltonian threshold graphs." Discrete Applied Mathematics 16, no. 1 (1987): 11–15. http://dx.doi.org/10.1016/0166-218x(87)90050-3.

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10

Manoussakis, Yannis. "Directed hamiltonian graphs." Journal of Graph Theory 16, no. 1 (1992): 51–59. http://dx.doi.org/10.1002/jgt.3190160106.

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11

Keshavarz-Kohjerdi, Fatemeh, and Ruo-Wei Hung. "Finding Hamiltonian and Longest (s,t)-Paths of C-Shaped Supergrid Graphs in Linear Time." Algorithms 15, no. 2 (2022): 61. http://dx.doi.org/10.3390/a15020061.

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A graph is called Hamiltonian connected if it contains a Hamiltonian path between any two distinct vertices. In the past, we proved the Hamiltonian path and cycle problems for general supergrid graphs to be NP-complete. However, they are still open for solid supergrid graphs. In this paper, first we will verify the Hamiltonian cycle property of C-shaped supergrid graphs, which are a special case of solid supergrid graphs. Next, we show that C-shaped supergrid graphs are Hamiltonian connected except in a few conditions. For these excluding conditions of Hamiltonian connectivity, we compute thei

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12

Nikoghosyan, Zh G. "Disconnected Forbidden Subgraphs, Toughness and Hamilton Cycles." ISRN Combinatorics 2013 (March 10, 2013): 1–4. http://dx.doi.org/10.1155/2013/673971.

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In 1974, Goodman and Hedetniemi proved that every 2-connected -free graph is hamiltonian. This result gave rise many other conditions for Hamilton cycles concerning various pairs and triples of forbidden connected subgraphs under additional connectivity conditions. In this paper we investigate analogous problems when forbidden subgraphs are disconnected which affects more global structures in graphs such as tough structures instead of traditional connectivity structures. In 1997, it was proved that a single forbidden connected subgraph in 2-connected graphs can create only a trivial class of h

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13

Vegi Kalamar, Alen. "Counting Traversing Hamiltonian Cycles in Tiled Graphs." Mathematics 11, no. 12 (2023): 2650. http://dx.doi.org/10.3390/math11122650.

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Recently, the problem of counting Hamiltonian cycles in 2-tiled graphs was resolved by Vegi Kalamar, Bokal, and Žerak. In this paper, we continue our research on generalized tiled graphs. We extend algorithms on counting traversing Hamiltonian cycles from 2-tiled graphs to generalized tiled graphs. We further show that, similarly as for 2-tiled graphs, for a fixed finite set of tiles, counting traversing Hamiltonian cycles can be performed in linear time with respect to the size of such graph, implying that counting traversing Hamiltonian cycles in tiled graphs is fixed-parameter tractable.

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14

Nebeský, Ladislav. "Hamiltonian colorings of graphs with long cycles." Mathematica Bohemica 128, no. 3 (2003): 263–75. http://dx.doi.org/10.21136/mb.2003.134180.

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15

Adame, Luis Enrique, Luis Manuel Rivera, and Ana Laura Trujillo-Negrete. "Hamiltonicity of Token Graphs of Some Join Graphs." Symmetry 13, no. 6 (2021): 1076. http://dx.doi.org/10.3390/sym13061076.

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Let G be a simple graph of order n with vertex set V(G) and edge set E(G), and let k be an integer such that 1≤k≤n−1. The k-token graph G{k} of G is the graph whose vertices are the k-subsets of V(G), where two vertices A and B are adjacent in G{k} whenever their symmetric difference A▵B, defined as (A∖B)∪(B∖A), is a pair {a,b} of adjacent vertices in G. In this paper we study the Hamiltonicity of the k-token graphs of some join graphs. We provide an infinite family of graphs, containing Hamiltonian and non-Hamiltonian graphs, for which their k-token graphs are Hamiltonian. Our result provides

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16

Wei, Bing. "Hamiltonian paths and hamiltonian connectivity in graphs." Discrete Mathematics 121, no. 1-3 (1993): 223–28. http://dx.doi.org/10.1016/0012-365x(93)90555-8.

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17

Klassen, Joel, and Barbara M. Terhal. "Two-local qubit Hamiltonians: when are they stoquastic?" Quantum 3 (May 6, 2019): 139. http://dx.doi.org/10.22331/q-2019-05-06-139.

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We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for n-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary n-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.

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18

M, Manjula, Leena N. Shenoy, and Sowmya Krishna. "Laceability Partition Dimension of Some Special Graphs." Indian Journal Of Science And Technology 17, no. 31 (2024): 3183–89. http://dx.doi.org/10.17485/ijst/v17i31.1955.

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Objectives: Laceability partition dimension of a connected graph is the minimum number of partitions of vertex set such that the subgraph induced by each partition is laceable in the case of a bipartite graph and random Hamiltonian laceable in case of non-bipartite graph . Methods: Mathematical Induction method and tracing Hamiltonian path. Findings: This study presents the laceability partition dimension (lpd) of some special graphs namely the Crown graph, Windmill graph, Dutch windmill graph, Cocktail party graph, shadow graph, and image graph. Novelty: This study discusses the laceability p

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19

Bueno, Letícia, Luerbio Faria, Figueiredo De, and Fonseca Da. "Hamiltonian paths in odd graphs." Applicable Analysis and Discrete Mathematics 3, no. 2 (2009): 386–94. http://dx.doi.org/10.2298/aadm0902386b.

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Lov?sz conjectured that every connected vertex-transitive graph has a Hamiltonian path. The odd graphs Ok form a well-studied family of connected, k-regular, vertex-transitive graphs. It was previously known that Ok has Hamiltonian paths for k ? 14. A direct computation of Hamiltonian paths in Ok is not feasible for large values of k, because Ok has (2k - 1, k - 1) vertices and k/2 (2k - 1, k - 1) edges. We show that Ok has Hamiltonian paths for 15 ? k ? 18. Instead of directly running any heuristics, we use existing results on the middle levels problem, therefore further relating these two fu

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20

Hopkins, Brian. "Hamiltonian paths on Platonic graphs." International Journal of Mathematics and Mathematical Sciences 2004, no. 30 (2004): 1613–16. http://dx.doi.org/10.1155/s0161171204307118.

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We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the2-holed torus is topologically uniquely Hamiltonian.

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21

SHERMAN, DAVID, MING TSAI, CHENG-KUAN LIN, et al. "4-ORDERED HAMILTONICITY FOR SOME CHORDAL RING GRAPHS." Journal of Interconnection Networks 11, no. 03n04 (2010): 157–74. http://dx.doi.org/10.1142/s0219265910002787.

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A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an infinite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997 by Ng and Schultz.13At the time, the only known examples were K4and K3,3. Some progress was made in 2008 by Mészáros,12when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover, an infinite class

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22

Keshavarz-Kohjerdi, Fatemeh, and Alireza Bagheri. "Hamiltonian Paths in Some Classes of Grid Graphs." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/475087.

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The Hamiltonian path problem for general grid graphs is known to be NP-complete. In this paper, we give necessary and sufficient conditions for the existence of Hamiltonian paths inL-alphabet,C-alphabet,F-alphabet, andE-alphabet grid graphs. We also present linear-time algorithms for finding Hamiltonian paths in these graphs.

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23

Manesh, Silviya. "K-ordered Hamiltonian Graphs." Indian Journal of Science and Technology 7, is3 (2014): 28–29. http://dx.doi.org/10.17485/ijst/2014/v7sp3.8.

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24

Arguello, Anahy Santiago, and Juan José Montellano-Ballesteros. "Hamiltonian normal Cayley graphs." Discussiones Mathematicae Graph Theory 39, no. 3 (2019): 731. http://dx.doi.org/10.7151/dmgt.2214.

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25

Zamfirescu, Carol T. "$K_2$-Hamiltonian Graphs: I." SIAM Journal on Discrete Mathematics 35, no. 3 (2021): 1706–28. http://dx.doi.org/10.1137/20m1355252.

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26

LIU, ZHENHONG, YONGJIN ZHU, and FENG TIAN. "Hamiltonian Cycles in Graphs." Annals of the New York Academy of Sciences 576, no. 1 Graph Theory (1989): 367–76. http://dx.doi.org/10.1111/j.1749-6632.1989.tb16419.x.

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27

Funk, M., Bill Jackson, D. Labbate, and J. Sheehan. "2-Factor hamiltonian graphs." Journal of Combinatorial Theory, Series B 87, no. 1 (2003): 138–44. http://dx.doi.org/10.1016/s0095-8956(02)00031-x.

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28

Chang, Gerard J., and Xuding Zhu. "Pseudo-Hamiltonian-connected graphs." Discrete Applied Mathematics 100, no. 3 (2000): 145–53. http://dx.doi.org/10.1016/s0166-218x(99)00181-x.

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29

Heuberger, Clemens. "On hamiltonian Toeplitz graphs." Discrete Mathematics 245, no. 1-3 (2002): 107–25. http://dx.doi.org/10.1016/s0012-365x(01)00136-4.

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30

Xiong, Liming, and Zhanhong Liu. "Hamiltonian iterated line graphs." Discrete Mathematics 256, no. 1-2 (2002): 407–22. http://dx.doi.org/10.1016/s0012-365x(01)00442-3.

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31

Tong, Li-Da, Hao-Yu Yang, and Xuding Zhu. "Hamiltonian Spectra of Graphs." Graphs and Combinatorics 35, no. 4 (2019): 827–36. http://dx.doi.org/10.1007/s00373-019-02035-0.

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32

Amar, D., E. Flandrin, I. Fournier, and A. Germa. "Pancyclism in hamiltonian graphs." Discrete Mathematics 89, no. 2 (1991): 111–31. http://dx.doi.org/10.1016/0012-365x(91)90361-5.

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33

Yang, Zhenqi. "On F-Hamiltonian graphs." Discrete Mathematics 196, no. 1-3 (1999): 281–86. http://dx.doi.org/10.1016/s0012-365x(98)00216-7.

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34

Jeng-Jung, Wang, Hung Chun-Nan, and Hsu Lih-Hsing. "Optimal 1-hamiltonian graphs." Information Processing Letters 65, no. 3 (1998): 157–61. http://dx.doi.org/10.1016/s0020-0190(98)00004-0.

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35

Chen, Bor-Liang, and Ko-Wei Lih. "Hamiltonian uniform subset graphs." Journal of Combinatorial Theory, Series B 42, no. 3 (1987): 257–63. http://dx.doi.org/10.1016/0095-8956(87)90044-x.

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36

Georges, John P. "Non-hamiltonian bicubic graphs." Journal of Combinatorial Theory, Series B 46, no. 1 (1989): 121–24. http://dx.doi.org/10.1016/0095-8956(89)90012-9.

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37

Chartrand, Gary, Ladislav Nebeský, and Ping Zhang. "Hamiltonian colorings of graphs." Discrete Applied Mathematics 146, no. 3 (2005): 257–72. http://dx.doi.org/10.1016/j.dam.2004.08.007.

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38

Renzema, Willem, and Ping Zhang. "Hamiltonian labelings of graphs." Involve, a Journal of Mathematics 2, no. 1 (2009): 95–114. http://dx.doi.org/10.2140/involve.2009.2.95.

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39

Lai, Hong-Jian, and Yehong Shao. "Ons-Hamiltonian Line Graphs." Journal of Graph Theory 74, no. 3 (2013): 344–58. http://dx.doi.org/10.1002/jgt.21713.

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40

Paoli, M., W. W. Wong, and C. K. Wong. "Minimumk-hamiltonian graphs, II." Journal of Graph Theory 10, no. 1 (1986): 79–95. http://dx.doi.org/10.1002/jgt.3190100111.

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41

Chen, Guantao, and R. H. Schelp. "Hamiltonian graphs involving distances." Journal of Graph Theory 16, no. 2 (1992): 121–29. http://dx.doi.org/10.1002/jgt.3190160203.

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42

Gould, Ronald J., and Xingxing Yu. "On hamiltonian-connected graphs." Journal of Graph Theory 18, no. 8 (1994): 841–60. http://dx.doi.org/10.1002/jgt.3190180808.

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43

Ng, Lenhard, and Michelle Schultz. "k-ordered Hamiltonian graphs." Journal of Graph Theory 24, no. 1 (1997): 45–57. http://dx.doi.org/10.1002/(sici)1097-0118(199701)24:1<45::aid-jgt6>3.0.co;2-j.

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44

Wei, Bing, and Yongjin Zhu. "Hamiltonian ?-factors in graphs." Journal of Graph Theory 25, no. 3 (1997): 217–27. http://dx.doi.org/10.1002/(sici)1097-0118(199707)25:3<217::aid-jgt5>3.0.co;2-o.

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45

Kierstead, H. A., G. N. S�rk�zy, and S. M. Selkow. "Onk-ordered Hamiltonian graphs." Journal of Graph Theory 32, no. 1 (1999): 17–25. http://dx.doi.org/10.1002/(sici)1097-0118(199909)32:1<17::aid-jgt2>3.0.co;2-g.

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46

Merino, Arturo, Torsten Mütze, and Namrata. "Kneser graphs are Hamiltonian." Advances in Mathematics 468 (May 2025): 110189. https://doi.org/10.1016/j.aim.2025.110189.

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47

Takaoka, Asahi. "Complexity of Hamiltonian Cycle Reconfiguration." Algorithms 11, no. 9 (2018): 140. http://dx.doi.org/10.3390/a11090140.

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The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained from C i − 1 by a switch for each i with 1 ≤ i ≤ t , where a switch is the replacement of a pair of edges u v and w z on a Hamiltonian cycle with the edges u w and v z of G, given that u w and v z did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More pre

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48

Paulraja, P., and Kumar Sampath. "On hamiltonian decompositions of tensor products of graphs." Applicable Analysis and Discrete Mathematics 13, no. 1 (2019): 178–202. http://dx.doi.org/10.2298/aadm170803003p.

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Finding a hamiltonian decomposition of G is one of the challenging problems in graph theory. We do not know for what classes of graphs G and H, their tensor product G x H is hamiltonian decomposable. In this paper, we have proved that, if G is a hamiltonian decomposable circulant graph with certain properties and H is a hamiltonian decomposable multigraph, then G x H is hamiltonian decomposable. In particular, tensor products of certain sparse hamiltonian decomposable circulant graphs are hamiltonian decomposable.

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49

Jiang, Guisheng, Lifang Ren, and Guidong Yu. "Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index." Journal of Chemistry 2019 (November 15, 2019): 1–9. http://dx.doi.org/10.1155/2019/2047406.

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In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex. Firstly, we discuss balanced bipartite graphs with δG≥t, where δG is the minimum degree of G, and gain some sufficient conditions for the graphs to be traceable or Hamiltonian, respectively. Secondly, we discuss nearly balanced bipartite graphs with δG≥t and present some sufficient conditions for the graphs to be traceable. Thirdly, we discuss graphs with δG≥t and obtain some c

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50

Lv, Shengmei, and Liying Zhao. "Hamiltonian Indices of Three Classes of Graphs Obtained from Petersen Graph." Axioms 12, no. 6 (2023): 580. http://dx.doi.org/10.3390/axioms12060580.

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In this paper, we mainly consider the Hamiltonian indices of three classes of graphs obtained from Petersen graph, that is, the minimum integer m of m-time iterated line graph Lm(G) of these three classes of graphs such that Lm(G) is Hamiltonian. We show that the Hamiltonian indices of those graphs obtained by replacing every vertex of Petersen graph with a n-cycle or a complete graph of order n, or adding n pendant edges to each vertex of Petersen graph are both 2. In addition, we also study the situations of adding an edge to these three classes of graphs and obtain that their Hamiltonian in

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