Question #2d377

Nov 24, 2016

The graph is not bipartite.

Explanation:

A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color. After, grouping the vertices in two sets, if those vertices in each set are not interconnected, then the graph is bipartite.

Attached a graph realization with the same degree sequence with coloring. We can verify that it is not bipartite, because we can group $\left\{1 , 2 , 3\right\}$ in one set and $\left\{4 , 5 , 6 , 7\right\}$ in another set, but the vertices in this last set are interconnected.

Note also that vertices {6,7} are conected each to the remaining.

Follows an example of a bipartite graph