For an edge subset S of connected graph G, if G - S has only one perfect matching M, then S is called an anti-forcing set of M. The number of edges in a smallest anti-forcing set of M is the anti-forcing number of M, generally indicated by the symbol a f (G, M) . For a graph G, its anti-forcing spectrum is defined as the integer set Spec af (G ) := { af(G, M) : M is a perfect matching of G } . In this paper, we show that for a (4,6)-fullerene graph T n with cyclic edge-connectivity 3, Spec af (T n ) = [ n + 3 , 2 n + 4] . Moreover, we show that for any perfect matching M of a (4 , 6) -fullerene graph G, a minimum anti-forcing set S of M and each M-alternating facial boundary share exactly one edge. Applying this conclusion, we prove that the minimum anti-forcing number of a lantern structure (4,6)-fullerene of order n is L n 8 j + 2 , and Spec a f (B n ) = [ L n 8 j + 2 , L n (c) 2022 Elsevier Inc. All rights reserved.
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