# What is Euler graph in discrete mathematics?

## What is Euler graph in discrete mathematics?

MathematicsComputer EngineeringMCA. Euler Graph – A connected graph G is called an Euler graph, if there is a closed trail which includes every edge of the graph G. Euler Path – An Euler path is a path that uses every edge of a graph exactly once. An Euler path starts and ends at different vertices.

**What is Euler Graph Theorem?**

‘ Euler’s path theorem states this: ‘If a graph has exactly two vertices of odd degree, then it has an Euler path that starts and ends on the odd-degree vertices. Otherwise, it does not have an Euler path.

**How do you show a graph is Eulerian?**

Proof Let G(V, E) be a connected graph and let G be decomposed into cycles. If k of these cycles are incident at a particular vertex v, then d(v) = 2k. Therefore the degree of every vertex of G is even and hence G is Eulerian.

### What is Euler and Hamilton graph?

Definition. A cycle that travels exactly once over each edge in a graph is called “Eulerian.” A cycle that travels exactly once over each vertex in a graph is called “Hamiltonian.”

**What is Euler graph and Hamiltonian graph explain with example?**

A connected graph G is Eulerian if there is a closed trail which includes every edge of G, such a trail is called an Eulerian trail. A connected graph G is Hamiltonian if there is a cycle which includes every vertex of G; such a cycle is called a Hamiltonian cycle.

**What is the difference between Eulerian and Hamiltonian graph with examples?**

Important: An Eulerian circuit traverses every edge in a graph exactly once, but may repeat vertices, while a Hamiltonian circuit visits each vertex in a graph exactly once but may repeat edges.

## What is graph explain Euler & Hamiltonian graph with example?

A connected graph G is Eulerian if there is a closed trail which includes every edge of G, such a trail is called an Eulerian trail. Hamiltonian Cycle. A connected graph G is Hamiltonian if there is a cycle which includes every vertex of G; such a cycle is called a Hamiltonian cycle.

**What is Euler graph and Hamiltonian graph?**

**How do you know if it’s a Euler path?**

Euler paths are an optimal path through a graph. They are named after him because it was Euler who first defined them. By counting the number of vertices of a graph, and their degree we can determine whether a graph has an Euler path or circuit.