A conjecture of Biggs concerning the resistance of a distance-regular graph.
A family of tridiagonal pairs related to the quantum affine algebra .
A four-class association scheme derived from a hyperbolic quadric in .
A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices
A category generalizing Jaeger-Nomura algebra associated to a spin model is given. It is used to prove some equivalence among the four conditions by Jaeger-Nomura for spin models of index 2.
A matrix representation of graphs and its spectrum as a graph invariant.
A new estimate for the vertex number of an edge-regular graph.
A prolific construction of strongly regular graphs with the -e. c. property.
A quasi-spectral characterization of strongly distance-regular graphs.
Affine transformations of a Leonard pair.
Amply regular graphs and block designs.
An eigenvalue characterization of antipodal distance-regular graphs.
Approximating the isoperimetric number of strongly regular graphs.
Association schemes and MacWilliams dualities for generalized Niederreiter-Rosenbloom-Tsfasman posets [Book]
Association schemes of affine type over finite rings.
Asymptotic spectral distributions of distance k-graphs of large-dimensional hypercubes
We derive the asymptotic spectral distribution of the distance k-graph of N-dimensional hypercube as N → ∞.
Bounds for the Hückel energy of a graph.
Characters of finite quasigroups VII: permutation characters
Each homogeneous space of a quasigroup affords a representation of the Bose-Mesner algebra of the association scheme given by the action of the multiplication group. The homogeneous space is said to be faithful if the corresponding representation of the Bose-Mesner algebra is faithful. In the group case, this definition agrees with the usual concept of faithfulness for transitive permutation representations. A permutation character is associated with each quasigroup permutation representation,...
Combinatorial vs. algebraic characterizations of completely pseudo-regular codes.
Complex Hadamard Matrices contained in a Bose–Mesner algebra
Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric...
Crooked functions, bent functions, and distance regular graphs.