Question

Does the graph above have an Hamiltonian circuit, Hamiltonian path, or neither? Paths and Circuits Help

a.. Only a Hamiltonian Path
b. It has both a Hamiltonian Path and Hamiltonian Circuit
c.. It does not have either an Hamiltonian Path or an Hamiltonian Circuit​

Answer 1

(c) neither

Explanation:

A Hamiltonian Path visits every node once. A Hamiltonian Circuit is a loop that visits every node once.

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This graph cannot have a Hamiltonian Circuit, because it has a node with degree 1. It cannot be part of a loop.

The graph cannot have either a Hamiltonian Path or Circuit, because the nodes in the two triangles cannot all be visited only once. Getting into and out of the triangle requires visiting a node twice.

This graph has neither a path nor a circuit.