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For what values of n the graph K, has (a) An Eulerian circuit. (b) An Eulerian trail (c) A Hamiltonian cycle (d) A Hamiltonian path

User Kylc
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Final answer:

An Eulerian circuit is a path that visits every edge exactly once and starts and ends at the same vertex. For a graph K to have an Eulerian circuit, all the vertices must have even degrees.

Step-by-step explanation:

An Eulerian circuit is a path in a graph that visits every edge exactly once and starts and ends at the same vertex. For a graph K to have an Eulerian circuit, all the vertices in K must have even degrees.

An Eulerian trail is a path in a graph that visits every edge exactly once but starts and ends at different vertices. For a graph K to have an Eulerian trail, exactly two vertices in K must have odd degrees.

A Hamiltonian cycle is a cycle in a graph that visits every vertex exactly once. A Hamiltonian cycle exists in a graph if and only if every pair of non-adjacent vertices in K has a degree of at least 2.

A Hamiltonian path is a path in a graph that visits every vertex exactly once. A Hamiltonian path exists in a graph if and only if every pair of non-adjacent vertices in K has a degree of at least 1.

User Rong Nguyen
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