A QUANTUM ASPECT OF ASYMPTOTIC SPECTRAL ANALYSIS OF LARGE HAMMING GRAPHS

A quantum decomposition of the adjacency matrix of a Hamming graph is introduced on the basis of Euler's unicursal theorem. Each of the quantum compoments converges in a large scale limit to a linear combination of the annihilation, creation and number operators on a one-mode Boson Fock space as a variant of quantum central limit theorem. As an immediate consequence, asymptotic distribution of eigenvalues of the adjacency matrix is reproduced.