UGC-NET | UGC NET CS 2018 Dec – II | Question 32

The K-coloring of an undirected graph G=(V,E) is a function C: V➝{0,1,……,K-1} such that c(u)≠c(v) for every edge (u,v) ∈ E Which of the following is not correct ?
(A) G has no cycles of odd length
(B) G has cycle of odd length
(C) G is 2-colorable
(D) G is bipartite

Answer: (B)
Explanation: A bipartite graph is a special kind of graph with the following properties-

• It consists of two sets of vertices X and Y.
• The vertices of set X join only with the vertices of set Y.
• The vertices within the same set do not join.

Bipartite graphs may be characterized in several different ways:

• A graph is bipartite if and only if it does not contain an odd cycle.
• A graph is bipartite if and only if it is 2-colorable, (i.e. its chromatic number is less than or equal to 2).
• The spectrum of a graph is symmetric if and only if it’s a bipartite graph.

Option (B) is false.
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