Hamilton cycles and eigenvalues of graphs
WebSep 26, 2024 · A cycle (path) containing every vertex of a graph is called a Hamilton cycle (path) of the graph. Graph G is called a Hamilton graph if it has a Hamilton cycle, and then we also ... K. C., and Zhu, S. (2024). … WebAug 24, 2010 · In this paper we prove a sufficient condition for the existence of a …
Hamilton cycles and eigenvalues of graphs
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WebApr 6, 2024 · The Hamilton cycles of a graph generate a subspace of the cycle space called the Hamilton space. The Hamilton space of any connected Cayley graph on an abelian group is determined in this paper. View WebWhy Eigenvalues of Graphs? (more specifically) The technique is often efficient in counting structures, e.g., acyclic di- graphs, spanning trees, Hamiltonian cycles, independent sets, Eulerian orientations, cycle covers,k-colorings etc.. [Golin et …
WebLemma 5.3, the eigenvalues of Rare 2, 1 (three times), ... Hamilton cycles in random lifts of graphs, European J. Combin. 27(2006), 1282–1293. [7] P. Chebolu and A.M. Frieze, Hamilton cycles in random lifts of complete directed graphs, SIAM J. Discrete Math. 22(2008), 520–540. WebApr 1, 2008 · This condition is sharp: the complete bipartite graph T 2 (n) with parts of size ⌊ n / 2 ⌋ and ⌈ n / 2 ⌉ contains no odd cycles and its largest eigenvalue is equal to ⌊ n 2 / 4 ⌋. This condition is stable: if μ ( G ) is close to ⌊ n 2 / 4 ⌋ and G fails to contain a cycle of length t for some t ⩽ n / 321 , then G resembles T 2 ...
WebFeb 16, 2015 · odd path (cycle) of given length, and a Hamilton path (cycle) [9, 15, 18, 19, 23, 24]. In particular, sufficient spectral conditions for the existence of Hamilton paths and cycles receive ... Webdecompositions; random graphs; uniform hypergraphs; counting Hamilton cycles. …
WebApr 1, 2005 · A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient...
WebSep 5, 2015 · It's worth adding that the eigenvalues of the Laplacian matrix of a complete graph are 0 with multiplicity 1 and n with multiplicity n − 1. where D is the diagonal degree matrix of the graph. For K n, this has n − 1 on the diagonal, and − 1 everywhere else. The constant vector 1 is then an eigenvector with eigenvalue 0. birthday gifts for dad/grandpaWebMar 9, 2024 · We present these results in new forms, now stated in terms of structural … dan murphy\u0027s home delivery pricesWebJun 7, 2010 · An eigenvalue of a graph is said to be a main eigenvalue if it has an eigenvector not orthogonal to the main vector j = (1,1,…,1). In this paper we shall study some properties of main eigenvalues of a graph. birthday gifts for dad turning 50Webcycles in graphs. In 2007, Nikiforov gave a restatement of a result originally due to Nosal in [10] which asserts that a graph with large enough spectral radius must ... Bounds on graph eigenvalues II, Linear Algebra Appl.,427, (2007), 183{189. [5] V. Nikiforov, A spectral condition for odd cycles in graphs, Linear Algebra Appl., 428, (2008 ... birthday gifts for dad over 80WebMay 27, 2011 · The diameter and Laplacian eigenvalues of directed graphs. Electronic Journal of Combinatorics 13(4) (2006). Google Scholar; Frieze, A.M.: Loose Hamilton cycles in random 3-uniform hypergraphs. Electronic Journal of Combinatorics 17(28) (2010). Google Scholar; Hán, H., Schacht, M.: 3 Dirac-type results for loose Hamilton … dan murphy\u0027s greenhillsWebHamilton cycles in graphs and hypergraphs: an extremal perspective Abstract. As one of the most fundamental and well-known NP-complete problems, the ... [81] on Hamilton cycles in regular graphs which involves the ‘eigenvalue gap’. The conjecture itself would follow from the toughness conjecture. Conjecture2.7([81]). There is a constant C ... dan murphy\u0027s helplineWebThe algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of G. [1] This eigenvalue is greater than 0 if and only if G is a connected graph. birthday gifts for dad made by preschoolers