论文信息 - Strongly Regular Graphs with Maximal Energy

Strongly Regular Graphs with Maximal Energy

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1+?n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+?n)/2, (n+2?n)/4, (n+2?n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.

W. Haemers | Willem H. Haemers

[1] Brendan D. McKay,et al. Classification of regular two-graphs on 36 and 38 vertices , 2001, Australas. J Comb..

[2] L. Hogben. Handbook of Linear Algebra , 2006 .

[3] Qing Xiang,et al. Symmetric Bush-type Hadamard matrices of order $4m^4$ exist for all odd $m$ , 2005 .

[4] Andries E. Brouwer,et al. Strongly Regular Graphs , 2022 .

[5] J. Seidel. Strongly Regular Graphs with (—1, 1, 0) Adjacency Matrix Having Eigenvalue 3 , 1991 .

[6] C. Colbourn,et al. Handbook of Combinatorial Designs , 2006 .

[7] Vincent Moulton,et al. Maximal Energy Graphs , 2001, Adv. Appl. Math..

[8] R. Craigen,et al. Hadamard Matrices and Hadamard Designs , 2006 .

[9] Willem H. Haemers. Matrices and Graphs , 2005 .

[10] I. Gutman. The Energy of a Graph: Old and New Results , 2001 .

[11] R. Paley. On Orthogonal Matrices , 1933 .

[12] Mikhail H. Klin,et al. Switching of Edges in Strongly Regular Graphs I: A Family of Partial Difference Sets on 100 Vertices , 2003, Electron. J. Comb..

[13] Anton Betten,et al. Algebraic Combinatorics and Applications : Proceedings , 2001 .