Anti-Ramsey number of intersecting cliques

An edge-colored graph is called a rainbow graph if all its edges have distinct colors. The anti-Ramsey number $ar(n, G)$, for a graph G and a positive integer n, is defined as the minimum number of colors r such that every exact r-edge-coloring of the complete graph Kₙ contains at least one rainbow copy of G. A $(k, r)$-fan graph, denoted Fk, r, is a graph composed of k cliques each of size r, all intersecting at exactly one common vertex. In this paper, we determine ar(n, Fk, r) for n ≥ 256r¹⁶(k+1)⁵, k ≥ 1, and r ≥ 2.