According to a study by Erdős et al. in 1975, the anti-Ramsey number of a graph \(G\) , denoted as \(AR(n, G)\) , is defined as the maximum number of colors that can be used in an edge-coloring of the complete graph \(K_n\) without creating a rainbow copy of \(G\) . In this paper, we investigate the anti-Ramsey number under edge deletion and demonstrate that both decreasing and unchanging are possible outcomes. For three non-negative integers \(k\) , \(t\) , and \(n\) , let \(G = kP_4 \cup tP_2\) . Let \(E'\) be a subset of the edge set \(E(G)\) such that every endpoint of these edges has a degree of two in \(G\) . We prove that if one of the conditions (i) \(t \ge k + 1 \ge 2\) and \(n \ge 8k + 2t - 4\) ; (ii) \(k, t \ge 1\) and \(n = 4k + 2t\) ; (iii) \(k = 1\) , \(t \ge 1\) , and \(n \ge 2t + 4\) , occurs then the behavior of the anti-Ramsey number remains consistent when the edges in \(E'\) are removed from \(G\) , i.e., \(AR(n, G) = AR(n, G - E')\) . However, this is not the case when \(k \ge 2\) , \(t = 0\) , and \(n=4k\) . As a result, we calculate \(AR(n,kP_4 \cup tP_2)\) for the cases: (i) \(t \ge k + 1 \ge 2\) and \(n \ge 8k + 2t - 4\) ; (ii) \(k, t \ge 1\) and \(n = 4k + 2t\) ; (iii) \(k = 1\) , \(t \ge 0\) , and \(n \ge 2t + 4\) ; (iv) \(k \ge 1\) , \(t = 0\) , and \(n = 4k\) .
