Consider the undirected graph G defined as follows. The vertices of G are bit strings of length n. We have an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position (in other words, v can be obtained from u by flipping a single bit). The ratio of the chromatic number of G to the diameter of G is

**(A)** 1/(2^{n-a})

**(B)** 1/n

**(C)** 2/n

**(D)** 3/n

**Answer:** **(C)** **Explanation:** <!–The given graph is the definition of Hypercube graph

chromatic number for this =2

diameter = n

So, the ratio =2/n

–>

**Bipartite graph:-** A bipartite graph is a graph G(V,E) where vertices can be decomposed into two disjoint sets such that no two vertices within the same set are adjacent.

**Diameter of a graph:-** The longest shortest path in between any two vertices of a graph The given graph is a bipartite graph => chromatic number is equals to 2 The diameter of graph is equals to n because at most we need to traverse n-1 edges.

The ratio = 2/n

Refernce:https://en.wikipedia.org/wiki/Hypercube_graph

This solution is contributed by **Anil Saikrishna Devarasetty**

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