关键词: 仙人掌图, 全Mostar指标, 端块圈, 极值图

Abstract: By using graph transformation method, we determined the largest total Mostar index for n-order cactus graph G with k cycles, 
and characterized the corresponding extremal graphs, when 2n+k>18 and n≥3k+1,  Mo_t(G)≤2n²+3nk-6n-25k+k²+4, and its equal sign holds if and only if G is the graph composed of attaching k end-blocks of length 4 and (n-3k-1) pendant edges to a common vertex. Furthermore, by discussing the classification of  the remaining cactus graph, we obtained the second-largest total Mostar index and characterized the corresponding extremal graphs.

Key words: cactus graph, total Mostar index, end-block, extremal graph