(a) In a complete graph having odd number of vertices, how many edge disjoint Hamiltonian circuits exist? Explain.
Explanation
A complete graph is a graph in which every pair of distinct vertices is connected by a unique edge. A Hamiltonian circuit is a path in a graph that visits each vertex exactly once and returns to the starting vertex. In a complete graph with an odd number of vertices, the number of edges is odd, and thus the number of Hamiltonian circuits is also odd. Since each Hamiltonian circuit contains all vertices, no two Hamiltonian circuits can be edge-disjoint.
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