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This video tutorial discusses a graph theory question from 2009, focusing on the basics of working with graphs and specifically the degree sequence. Given a graph G with a degree sequence of 4 3 3 2 1 1, there are 6 vertices in G. To find the number of edges, sum up the degree sequence (14) and divide by 2, resulting in 7 edges. The tutorial also explores constructing the graph based on the given information.