Equienergetic self-complementary graphs

Indulal, Gopalapillai; Vijayakumar, A.

doi:10.1007/s10587-008-0059-y

Cited by 13 publications

(13 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was followed by the distance energy (based on the eigenvalues of the distance matrix), [37] normalized Laplacian energy (based on the eigenvalues of the normalized Laplacian matrix [38] which independently was introduced under the name of "Randić energy"), [39] etc. Consonni and Todeschini [40] defined the energy of any real symmetric matrix with eigenvalues 1 2 , , , n x x x  as Nikiforov extended the energy-concept to any matrix.…”

Section: The Graph Energy Delugementioning

confidence: 99%

“…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%

See 1 more Smart Citation

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

View full text Add to dashboard Cite

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.

show abstract

Section: The Graph Energy Delugementioning

confidence: 99%

Section: The Graph Energy Delugementioning

confidence: 99%

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

View full text Add to dashboard Cite

show abstract

“…For obvious reason Seidel cospectral graphs are Seidel equienergetic. Several results on equienergetic graphs [2,4,5,15,24,27,28,29,30,31], distance equienergetic graphs [14,23,26], Laplacian equienergetic graphs [8], equienergetic digraphs [17], skew equienergetic digraphs [1,25], equienergetic sigraphs [3,9,10,19] and equienergetic sidigraphs [21] were reported in the literature.…”

Section: Introductionmentioning

confidence: 99%

Seidel Equienergetic Graphs

Ramane

Gundloor

Hosamani³

2016

BMSA

View full text Add to dashboard Cite

Abstract. The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are -1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE(G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G 1 and G 2 are said to be Seidel equienergetic if SE(G 1 ) = SE(G 2 ). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12.

show abstract

“…There are several papers on construction of equienergetic graphs (see [2,3,10,11,12,13,15,16,17,19]). The objective of this paper is to construct noncospectral equienergetic signed graphs of same order which are unbalanced.…”

Section: Introductionmentioning

confidence: 99%

Equienergetic net-regular signed graphs

Nayak¹

2014

ijcms

View full text Add to dashboard Cite

The concept of energy is recently generalized to signed graphs i.e. the sum of the absolute values of the eigenvalues of a signed graph Σ. Many authors have constructed non-cospectral equienergeic graphs. In this paper, we established the spectra of heterogeneous unbalanced netregular signed complete graphs. Then, we give a method to construct an infinite pairs of unbalanced, non-cospectral, equienergetic, net-regular signed graphs of the same order.Mathematics Subject Classification: 05C22, 05C50

show abstract

Equienergetic self-complementary graphs

Cited by 13 publications

References 7 publications

The Total π-Electron Energy Saga

The Total π-Electron Energy Saga

Seidel Equienergetic Graphs

Equienergetic net-regular signed graphs

Contact Info

Product

Resources

About