The triangular graph T_n = L(K_n) is the line graph of the complete graph K_n. The vertices of T_n may be identified with the 2-subsets of {1, 2, ..., n} that are adjacent iff the 2-subsets have a nonempty intersection, namely the Johnson graph J(n, 2). The triangular graphs are distance-regular and geometric. Chang (1959, 1960) and Hoffman showed that if G is a strongly regular graph on the parameters (ν, k, λ, μ) = (n(n - 1)/2, 2(n - 2), n - 2, 4) with n>=4, then if n!=8, G is isomorphic to the triangular graph T_n. If n = 8, then G is isomorphic to one of three graphs known as the Chang graphs or to T_8.

Chang graphs | cospectral graphs | determined by spectrum | Johnson graph | lattice graph | square graph | triangle graph | triangular grid graph