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Relevant bibliographies by topics / Eulerian graph theory. Hamiltonian graph theory

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Journal articles

Academic literature on the topic 'Eulerian graph theory. Hamiltonian graph theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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Journal articles on the topic "Eulerian graph theory. Hamiltonian graph theory"

1

Tamizh Chelvam, T., and S. Anukumar Kathirvel. "Generalized unit and unitary Cayley graphs of finite rings." Journal of Algebra and Its Applications 18, no. 01 (2019): 1950006. http://dx.doi.org/10.1142/s0219498819500063.

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Let [Formula: see text] be a finite commutative ring with nonzero identity and [Formula: see text] be the set of all units of [Formula: see text] The graph [Formula: see text] is the simple undirected graph with vertex set [Formula: see text] in which two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if there exists a unit element [Formula: see text] in [Formula: see text] such that [Formula: see text] is a unit in [Formula: see text] In this paper, we obtain degree of all vertices in [Formula: see text] and in turn provide a necessary and sufficient co

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2

Medvedev, Paul, and Mihai Pop. "What do Eulerian and Hamiltonian cycles have to do with genome assembly?" PLOS Computational Biology 17, no. 5 (2021): e1008928. http://dx.doi.org/10.1371/journal.pcbi.1008928.

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Many students are taught about genome assembly using the dichotomy between the complexity of finding Eulerian and Hamiltonian cycles (easy versus hard, respectively). This dichotomy is sometimes used to motivate the use of de Bruijn graphs in practice. In this paper, we explain that while de Bruijn graphs have indeed been very useful, the reason has nothing to do with the complexity of the Hamiltonian and Eulerian cycle problems. We give 2 arguments. The first is that a genome reconstruction is never unique and hence an algorithm for finding Eulerian or Hamiltonian cycles is not part of any as

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3

Metsidik, Metrose. "Eulerian and Even-Face Graph Partial Duals." Symmetry 13, no. 8 (2021): 1475. http://dx.doi.org/10.3390/sym13081475.

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Eulerian and bipartite graph is a dual symmetric concept in Graph theory. It is well-known that a plane graph is Eulerian if and only if its geometric dual is bipartite. In this paper, we generalize the well-known result to embedded graphs and partial duals of cellularly embedded graphs, and characterize Eulerian and even-face graph partial duals of a cellularly embedded graph by means of half-edge orientations of its medial graph.

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Broersma, H. J. "A note on K4-closures in hamiltonian graph theory." Discrete Mathematics 121, no. 1-3 (1993): 19–23. http://dx.doi.org/10.1016/0012-365x(93)90533-y.

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Broersma, H. J. "On some intriguing problems in hamiltonian graph theory—a survey." Discrete Mathematics 251, no. 1-3 (2002): 47–69. http://dx.doi.org/10.1016/s0012-365x(01)00325-9.

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6

Li, Hao. "Generalizations of Dirac’s theorem in Hamiltonian graph theory—A survey." Discrete Mathematics 313, no. 19 (2013): 2034–53. http://dx.doi.org/10.1016/j.disc.2012.11.025.

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7

Ceulemans, A., E. Lijnen, P. W. Fowler, R. B. Mallion, and T. Pisanski. "Graph theory and the Jahn–Teller theorem." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (2011): 971–89. http://dx.doi.org/10.1098/rspa.2011.0508.

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The Jahn–Teller (JT) theorem predicts spontaneous symmetry breaking and lifting of degeneracy in degenerate electronic states of (nonlinear) molecular and solid-state systems. In these cases, degeneracy is lifted by geometric distortion. Molecular problems are often modelled using spectral theory for weighted graphs, and the present paper turns this process around and reformulates the JT theorem for general vertex- and edge-weighted graphs themselves. If the eigenvectors and eigenvalues of a general graph are considered as orbitals and energy levels (respectively) to be occupied by electrons,

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8

Blanco, Rocío, and Melody García-Moya. "Graph Theory for Primary School Students with High Skills in Mathematics." Mathematics 9, no. 13 (2021): 1567. http://dx.doi.org/10.3390/math9131567.

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Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide

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9

Thomassen, Carsten. "On the Number of Hamiltonian Cycles in Bipartite Graphs." Combinatorics, Probability and Computing 5, no. 4 (1996): 437–42. http://dx.doi.org/10.1017/s0963548300002182.

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We prove that a bipartite uniquely Hamiltonian graph has a vertex of degree 2 in each color class. As consequences, every bipartite Hamiltonian graph of minimum degree d has at least 21−dd! Hamiltonian cycles, and every bipartite Hamiltonian graph of minimum degree at least 4 and girth g has at least (3/2)g/8 Hamiltonian cycles. We indicate how the existence of more than one Hamiltonian cycle may lead to a general reduction method for Hamiltonian graphs.

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10

Horák, Peter, Tomáš Kaiser, Moshe Rosenfeld, and Zdeněk Ryjáček. "The Prism Over the Middle-levels Graph is Hamiltonian." Order 22, no. 1 (2005): 73–81. http://dx.doi.org/10.1007/s11083-005-9008-7.

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