Question: Does there exist a multigraph G of order 8 such that Minimum d(G) = 0 while Maximum d(G) = 7? What if ‘multigraph G’ is replaced by ‘graph G’?
Answer: such multigraph does not exist, but graph?
Question: Does there exist a multigraph G of order 8 such that Minimum d(G) = 0 while Maximum d(G) = 7? What if ‘multigraph G’ is replaced by ‘graph G’?
Answer: such multigraph does not exist, but graph?
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.