Final answer:
To determine if a graph is bipartite, one must check if the vertices can be split into two sets with no adjacent vertices from the same set. By attempting to color the graph with two colors, one can identify if there is an even or odd cycle, where an odd cycle would indicate a non-bipartite graph.
Step-by-step explanation:
The question asks us to determine whether a graph is bipartite or not. To address this, we need to understand that a bipartite graph is one where the set of vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent.
We can often determine if a graph is bipartite by attempting to color the vertices with two colors, where each color represents one of the disjoint sets and adjacent vertices must be of opposite colors. If we can accomplish this without any conflicts, the graph is bipartite. Otherwise, the presence of an odd-length cycle would indicate that the graph is not bipartite, as you cannot color an odd cycle with two colors without a conflict.
Without a specific graph to evaluate, we cannot detail the exact sets or odd-length cycle. However, the process involves examining the graph, starting at one vertex, and alternating colors or sets as you move through adjacent vertices. Once you've attempted to color or set all vertices, you'll be able to determine if the graph is bipartite or not based on any conflicts that arise.