Question

A ______ in a graph G is a circuit which consists of every vertex (except first/last vertex) of G exactly once.

(a) Euler path

(b) Hamiltonian path

(c) Planar graph

(d) Path complement graph

The question was asked in homework.

Question is from Different Path in a Graph in section Graphs of Discrete Mathematics

Answer 1

Right option is (b) Hamiltonian path

For explanation: The Eulerian path in a graph say, G is a walk from one vertex to another, that can pass through all vertices of G as well as traverses exactly once every edge of G. Therefore, an Eulerian path can not be a circuit. A Hamiltonian path is a walk that contains every vertex of the graph exactly once. Hence, a Hamiltonian path is not a circuit.