▎ 摘　　要

A method of construction of graphs for extended graphene sheets of the formula C6n2H6n, n = 1, 2, 3, ..., maintaining six-fold symmetry has been developed. It has been shown that their adjacency matrices, which are of size 6n(2)x6n(2), can be reduced to n(2)xn(2) matrices by exploring rotational symmetry and the reduced matrix can be easily written down as the adjacency matrix of a directed graph with n(2) vertices (called 'reduced graph' in this article). A scheme for drawing the reduced graph is devised and from this the graph eigenvalues can be easily determined. It has been shown that the HOMO-LUMO energy gap of the pi-MOs decreases as n increases, and an almost gapless graphene sheet (Delta E = E-LUMO - E-HOMO = 4.5x10(-10) beta, where beta = resonance integral between two adjacent sp(2)-C atoms) begins to form at 6x20(2) carbon atoms arranged in a 2-dimensional hexagonal lattice.