Let n be an even number, and form an undirected graph with nvertices numbered from 0 to n – 1, by adding edges connecting eachvertex numbered i to the three vertices numbered i – 1 (mod n), i +1 (mod n), and i + n/2 (mod n). For instance, when n is four, thisgraph can be drawn using the sides and diagonals of a square.
(a) For which values of n is this graph bipartite?
(b) When the graph is bipartite, describe (as a function of i)which vertices are on the two sides of its bipartition.
(c) When the graph is not bipartite,
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