Does there exist a multigraph $G$ of order $8$ such that the minimal $d(G) = 0$ while maximal $d(G) = 7$? What if ‘multigraph $G$’ is replaced by ‘graph $G$’?
Answer: such multigraph does not exist, but graph?
2026-03-25 07:38:28.1774424308
Difference between graph and multigraph
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If a graph, G, has order 8, it has 8 vertices. If maximum d(G) = 7, it has a vertex, v, of degree 7.
Then, vertex v is connected to 7 neighbors, each of which has degree at least 1 because they are at least connected to v. So, minimum d(G) must be at least 1.
So, there is no graph that fits your criteria.