2026-321

Let \(G=(V,E)\) be a simple undirected graph, meaning that it has no self-loops (edges of the form \((v, v)\)) and no multiple edges between the same pair of vertices.

For such a graph we can define its degree sequence, as the sequence of its vertex degrees in nonincreasing order..

For example, the graph shown below has degree sequence

(3,1,1,1)

For each of the following statements, determine whether it is True (T) or False (F).

i) \( (2,2) \) is the degree sequence of several nonisomorphic graphs.
ii) \( (2,2,2) \) is the degree sequence of exactly one graph, up to isomorphism.
iii) \( (2,2,2,2,2,2) \) is the degree sequence of exactly one graph, up to isomorphism.

Alternatives

a) FTF
b) FTT
c) TFT
d) TTF
e) None of the above

Original idea by: Luis Alberto Vásquez Vargas