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To find a **minimum-weight spanning tree** (MST) in the given weighted graph, let’s apply Kruskal’s algorithm step by step: *** ## Step 1: List All Edges With Weights Let’s label the vertices for reference: $$v_1, v_2, v_3, v_4, v_5, v_6, v_7, v_8$$. List the edges and their weights (read from the image): - $$ v_1v_2: 3 $$ - $$ v_1v_6: 6 $$ - $$ v_1v_7: 5 $$ - $$ v_2v_3: 2 $$ - $$ v_2v_6: 6 $$ - $$ v_3v_4: 1 $$ - $$ v_3v_5: 2 $$ - $$ v_3v_6: 4 $$ - $$ v_4v_5: 6 $$ - $$ v_4v_8: 8 $$ - $$ v_5v_6: __________ __________ ____ _________ __________ _______ _____ _______ ______.
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