October 29, 2023
October 29, 2023
October 29, 2023
###### NTA UGC NET JUNE-2023 Paper-2
October 29, 2023

Consider the graph given below: The two distinct sets of vertices, which make the graph bipartite are:

Question 4 Explanation:
A bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.
→ The two sets U and V may be thought of as a coloring of the graph with two colors.
Option A: FALSE because V​ 5​ , V​ 7​ and V​ 3​ are adjacent. So, it not not bipartite graph.

Option-B FALSE because V​ 5​ , V​ 6​ and V​ 2​ are adjacent. So, it not not bipartite graph.

Option-C TRUE because it follows properties of bipartied and no two colours are adjacent.

Option-D FALSE because because V​ 4​ , V​ 6​ and V​ 8​ are adjacent. So, it not not bipartite graph.
(v​ 1​ , v​ 4​ , v​ 6​ ); (v​ 2​ , v3​ , v​ 5​ , v​ 7​ , v​ 8​ )
(v​ 1​ , v​ 7​ , v​ 8​ ); (v​ 2​ , v​ 3​ , v​ 5​ , v​ 6​ )
(v​ 1​ , v​ 4​ , v​ 6​ , v​ 7​ ); (v​ 2​ , v​ 3​ , v​ 5​ , v​ 8​ )
(v​ 1​ , v​ 4​ , v​ 6​ , v​ 7​ , v​ 8​ ); (v​ 2​ , v​ 3​ , v​ 5​ )