Algebraic characterizations of regularity properties in bipartite graphs

European Journal of Combinatorics - Tập 34 - Trang 1223-1231 - 2013
Aida Abiad1, Cristina Dalfó1, Miquel Àngel Fiol1
1Dept. de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Barcelona, Catalonia, Spain

Tài liệu tham khảo

Bannai, 1984

Biggs, 1993

Brouwer, 1989

Brouwer, 2012

Cámara, 2009, Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes, Electron. J. Combin., 16, #R83, 10.37236/172

Cvetković, 1982

Dalfó, 2009, On k-walk-regular graphs, Electron. J. Combin., 16, #R47, 10.37236/136

Dalfó, 2012, Dual concepts of almost distance-regularity and the spectral excess theorem, Discrete Math., 10.1016/j.disc.2012.03.003

Fiol, 2002, Algebraic characterizations of distance-regular graphs, Discrete Math., 246, 111, 10.1016/S0012-365X(01)00255-2

Fiol, 1997, From local adjacency polynomials to locally pseudo-distance-regular graphs, J. Combin. Theory Ser. B, 71, 162, 10.1006/jctb.1997.1778

Fiol, 2001, Boundary graphs: the limit case of a spectral property, Discrete Math., 226, 155, 10.1016/S0012-365X(00)00184-9

Godsil, 1993

Godsil, 2001, vol. 207

Hoffman, 1963, On the polynomial of a graph, Amer. Math. Monthly, 70, 30, 10.2307/2312780

Rowlinson, 1997, Linear algebra, vol. 5, 86

van Dam, 2008, The spectral excess theorem for distance-regular graphs: a global (over)view, Electron. J. Combin., 15, #R129, 10.37236/853

van Dam, 1995, Regular graphs with four eigenvalues, Linear Algebra Appl., 226–228, 139, 10.1016/0024-3795(94)00346-F

E.R. van Dam, J.H. Koolen, H. Tanaka, Distance-regular graphs, Manuscript, 2012. Available online at http://lyrawww.uvt.nl/~evandam/files/drg.pdf.

van Dam, 2005, Combinatorial designs with two singular values II, partial geometric designs, Linear Algebra Appl., 396, 303, 10.1016/j.laa.2004.09.015