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Does there exist a simple graph with 7 vertices having degrees 1 3 3 4 5 6 6?
Wiki User
∙ 12y ago
No.
Since the graph is simple, none of the vertices connect to themselves - that is, there are no arcs that loop back on themselves. Then the two vertices with degree 6 must connect to all the other vertices. Therefore there can be no vertex with less than two arcs [ to these two vertices]. So a vertex with degree 1 cannot be part of the graph.
Wiki User
∙ 12y ago
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