An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?(a) 1/2^101(b) 1/50(c) 1/100(d) 1/20The question was asked during an interview.The query is from Graphs Properties topic in section Graphs of Discrete Mathematics

An undirected graph G has bit strings of length 100 in its vertices an

1.	An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?(a) 1/2^101(b) 1/50(c) 1/100(d) 1/20The question was asked during an interview.The query is from Graphs Properties topic in section Graphs of Discrete Mathematics
Answer» Right CHOICE is (b) 1/50 Explanation: For the given condition we can simply design a K-Map and mark an EDGE between every two adjacent cells in K-map. Hence, that will give us a Bipartite graph and CHROMATIC number for this = 2. Hence the ratio is 2/n=2/100=1/50 and the given graph is actually a hypercube graph.

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