The skew energy of random oriented graphs

Chen, Xiaolin; Li, Xueliang; Lian, Huishu

doi:10.1016/j.laa.2013.02.007

Cited by 18 publications

(16 citation statements)

References 14 publications

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“…Note that the energy of a randomly chosen k-regular graph of order n is almost equal to the skew energy of a randomly chosen k-regular oriented graph of order n (Theorem 4.3 of [5]). This is not very surprising, as k-regular graphs of large order locally are trees, and the skew energy of oriented trees is equal to the energy of the underlying unoriented tree.…”

Section: The Energy Of Random Regular Graphsmentioning

confidence: 99%

Remarks on the energy of regular graphs

Nikiforov¹

2016

Linear Algebra and its Applications

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The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. This note is about the energy of regular graphs. It is shown that graphs that are close to regular can be made regular with a negligible change of the energy. Also a k-regular graph can be extended to a k-regular graph of a slightly larger order with almost the same energy. As an application, it is shown that for every sufficiently large n, there exists a regular graph G of order n whose energy G * satisfies G * > 1 2 n 3/2 − n 13/10 .Several infinite families of graphs with maximal or submaximal energy are given, and the energy of almost all regular graphs is determined.

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Section: The Energy Of Random Regular Graphsmentioning

confidence: 99%

Remarks on the energy of regular graphs

Nikiforov¹

2016

Linear Algebra and its Applications

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“…For A n,b (p) the mean is a := Eξ k = p and the variance is σ 2 := E|ξ k − a| 2 = p (1 − p). Therefore, formula (7) becomes…”

Section: Comparison Of Random Graph Energiesmentioning

confidence: 99%

The asymptotic trace norm of random circulants and the graph energy

Koshkin

2016

Discuss. Math. Probability and Statistics

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We compute the expected normalized trace norm (matrix/graph energy) of random symmetric band circulant matrices and graphs in the limit of large sizes, and obtain explicit bounds on the rate of convergence to the limit, and on the probabilities of large deviations. We also show that random symmetric band Töeplitz matrices have the same limit norm assuming that their band widths remain small relative to their sizes. We compare the limit norms across a range of related random matrix and graph ensembles.

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“…Later, Gong and Xu [3] characterized the 3-regular oriented graphs with optimum skew energy. Recently, we [2] studied the skew energy of random oriented graphs.…”

Section: Introductionmentioning

confidence: 99%

4-Regular oriented graphs with optimum skew energy

Chen

Lian

2013

Linear Algebra and its Applications

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Let G be a simple undirected graph, and G σ be an oriented graph of G with the orientation σ and skew-adjacency matrix S(G σ ). The skew energy of the oriented graph G σ , denoted, is defined as the sum of the absolute values of all the eigenvalues of S(G σ ).In this paper, we characterize the underlying graphs of all 4-regular oriented graphs with optimum skew energy and give orientations of these underlying graphs such that the skew energy of the resultant oriented graphs indeed attain optimum. It should be pointed out that there are infinitely many 4-regular connected optimum skew energy oriented graphs, while the 3-regular case only has two graphs: K 4 the complete graph on 4 vertices and Q 3 the hypercube.

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The skew energy of random oriented graphs

Cited by 18 publications

References 14 publications

Remarks on the energy of regular graphs

Remarks on the energy of regular graphs

The asymptotic trace norm of random circulants and the graph energy

4-Regular oriented graphs with optimum skew energy

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