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?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
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.