The skew energy of a digraph

Adiga, Chandrashekara; Balakrishnan, R.; So, Wasin

doi:10.1016/j.laa.2009.11.034

Cited by 127 publications

(122 citation statements)

References 4 publications

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“…In reality, the number of existing graph energies may be still greater, and more such will for sure appear in the future. 1) (ordinary) graph energy [12] 2) extended adjacency energy [30] 3) Laplacian energy [36] 4) energy of matrix [41] 5) minimum robust domination energy [49] 6) energy of set of vertices [50] 7) distance energy [37] 8) Laplacian-energy-like invariant [51] 9) Consonni-Todeschini energies [40] 10) energy of (0,1)-matrix [52] 11) incidence energy [53] 12) maximum-degree energy [54] 13) skew Laplacian energy [55] 14) oriented incidence energy [56] 15) skew energy [57] 16) Randić energy [39] 17) normalized Laplacian energy [38] 18) energy of matroid [58] 19) energy of polynomial [42] 20) Harary energy [59] 21) sum-connectivity energy [60] 22) second-stage energy [61] 23) signless Laplacian energy [62] 24) PI energy [63] 25) Szeged energy [64] 26) He energy [65] 27) energy of orthogonal matrix [66] 28) common-neighborhood energy [67] 29) matching energy [43] 30) Seidel energy [68] 31) ultimate energy [69] 32) minimum-covering energy [70] 33) resistance-distance energy [71] 34) Kirchhoff energy [72] 35) color energy [73] 36) normalized incidence energy [74] 37) Laplacian distance energy [75] 38) Laplacian incidence energy [76] 39) Laplacian minimum dominating energy …”

Section: The Graph Energy Delugementioning

confidence: 99%

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

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Abstract:The total π-electron energy, as calculated within the Hückel tight-binding molecular orbital approximation, is a quantum-theoretical characteristic of conjugated molecules that has been conceived as early as in the 1930s. In 1978, a minor modification of the definition of total π-electron energy was put forward, that made this quantity interesting and attractive to mathematical investigations. The concept of graph energy, introduced in 1978, became an extensively studied graph-theoretical topic, with many hundreds of published papers. A great variety of graph energies is being considered in the current mathematical-chemistry and mathematical literature. Recently, some unexpected applications of these graph energies were discovered, in biology, medicine, and image processing.We provide historic, bibliographic, and statistical data on the research on total π-electron energy and graph energies, and outline its present state of art. The goal of this survey is to provide, for the first time, an as-complete-as-possible list of various existing variants of graph energy, and thus help the readers to avoid getting lost in the jungle of references on this topic.

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Section: The Graph Energy Delugementioning

confidence: 99%

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

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“…Then there has exactly one pathlike graph if n = 3, namely, P 1,0 = P 3 , and exactly two pathlike graphs if n = 4, namely, P 1,1 and P 2,0 = K 1,3 . By a direct calculation, we have…”

Section: Lemma 1 Let G σ Be An Arbitrary Oriented Graph On N Verticementioning

confidence: 99%

“…Let G σ be an oriented graph with vertex set {v 1 Where i = √ −1 (Note that the definition is slightly different from the one of the normal skew-adjacency matrix given by Adiga et al [1]). Since S(G σ ) is an Hermitian matrix, the eigenvalues…”

Section: Introductionmentioning

confidence: 99%

Oriented bicyclic graphs whose skew spectral radius does not exceed 2

Jia-Hui¹,

Xu²

2013

Proceedings of 3rd International Conference on Multimedia Technology(ICMT-13)

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“…The sum ε(G) := n i=1 |λ i (G)| is known as the energy of the graph G. The concept of the energy of a graph was introduced by Gutman [14] and was recently generalized to oriented graphs as skew energy by Adiga, Balakrishnan and So in [1]. If λ i (G) (i = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%