Graph theory

Math

Eulerian circuit

is a circuit which traverse every edge exactly once

Eulerian trial

is a trail that traverses every edge exactly once, but does not start and end at the same vertex

Semi - Eulerian

if there are exactly two vertices of odd edges

Hamiltonian path

Is a path that visits each vertex exactly once, but does not end at the same vertex

Aim of Chinese Postman Problem

To find the shortest possible route that travels along every edge of a network at least once and returns to the starting point.

Aim of Traveling salesman problem

To find the shortest possible route that visits every vertex exactly once and returns to the starting point.

Hamiltonian cycle

Is a cycle which visits each vertex except the starting and ending vertical exactly once