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Question

A graph G with n nodes is biparatite. If it contains

A
n edges
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B
a cycle of odd length
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C
no cycle of odd length
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D
n2 edges
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Solution

The correct option is D no cycle of odd length

A graph G with n nodes is biparatite. If it contains no cycle of odd length.

A cycle is a path with the same first and last vertex. The length of the cycle is the number of edges that it contains, and a cycle is odd if it contains an odd number of edges. A cycle with an odd number of vertices is called an odd cycle.

A bipartite graph is a graph whose vertices can be divided into two disjoint sets U and V such that every edge connects a vertex in U to one in V; that is, U and V are independent sets.

A graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from mathematics; specifically, the field of graph theory. The vertices may be part of the graph structure, or may be external entities represented by integer indices or references.


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