Input

Error in problem solving.

Please enter the input according to the guideline. If you have any question, please email optimizationcity@gmail.com .

Output

Introduction

In graph theory, an Eulerian circuit is a path that starts from a vertex and passes all edges once (and only once) and returns to the same vertex. If the path passes through all edges but does not return to its first place, it is called an Eulerian path.

There is no specific software to find the Eulerian circuit, and to find this circuit, the existing algorithms must be coded in one of the programming languages. The Optimization City group has developed an online solver for the problem of finding the Eulerian circuit. Below is a guide for using this online solver.

Instruction of using online solver of the Eulerian circuit

The GUI of the online solver of this problem is as follows.

Problem input

To find the optimal solution to the problem of finding the Eulerian circle, the required inputs are as follows:

n: the number of desired graph nodes.

m: the number of edges of the desired graph.

nodei: is a vector with m+1 components, where the i-th component represents the initial node of the i-th edge.

nodej: is a vector with m+1 components, where the i-th component represents the terminal node of the i-th edge.

Example: Consider the graph below.

Determine the Euler circuit of the above graph.

Solution:

Entering information in the online solver of the euler circuit is as follows

After entering the data, we click on the RUN button.

The result of running the algorithm is as follows.

In the output part, it reports the edges that exist in the Euler circuit.