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 F₊, ₑ, 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, F₊, ₑ) for n 256r^16 (k+1) ⁵, k 1, and r 2.
Lu et al. (Thu,) studied this question.