Ciclo Euleriano? (0/1)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The 'Eulerian Cycle? (0/1)' calculator checks if a graph is Eulerian, meaning it allows a cycle that traverses each edge exactly once, returning to the starting vertex. It does this by verifying if all vertices in the graph have even degrees (an even number of connected edges). This concept is crucial in graph theory and finds applications in optimized routing, such as delivery logistics or transportation networks.
The calculator operates based on Euler's Theorem: a connected graph has an Eulerian cycle if and only if every vertex has an even degree. If the graph is disconnected or has vertices with odd degrees, the result will be negative. Users must ensure accurate input data, including all edges and connections, to guarantee reliable results.
Use this tool for planning routes without repetition, analyzing network flows, or theoretical graph studies. Avoid applying it to disconnected graphs or scenarios where visiting vertices, rather than edges, is the priority. The accuracy of the results depends entirely on the correctness of the input data.
Frequently asked questions
What is an Eulerian cycle?
It is a closed path that traverses all edges of a graph exactly once, returning to the starting point. It requires all vertices to have even degrees and the graph to be connected.
How does the calculator work?
It checks if all vertices in the provided graph have even degrees and if the graph is connected. If both conditions are met, it returns 1 (yes); otherwise, 0 (no).
Why is connectivity important for an Eulerian cycle?
Even if all vertices have even degrees, if the graph is disconnected (with isolated sections), it's impossible to form a single cycle covering all edges.
Is there a difference between an Eulerian path and an Eulerian cycle?
Yes. An Eulerian path starts and ends at different vertices (with exactly two vertices of odd degrees), while an Eulerian cycle forms a closed loop (all vertices with even degrees).