Two linear preserver problems on graphs

Abstract

Let n, t, k be integers such that 3 ≤ t, k ≤ n. Denote by Gn the set of graphs with vertex set {1, 2, . . . , n}.  In this paper, the complete linear transformations on Gn mapping Kt-free graphs to Kt-free graphs are characterized. The complete linear transformations on G_nmapping C_k-free graphs to C_k-free graphs are also characterized when n ≥ 6.