self doubt

Question

Is it necessary that euler graph should always be simple graph?

Answer 1

No. Not Necessary. Euler Graph simply means a Graph with Euler Path/Circuit in it (Cover Every Edge Exactly Once). So, You can take a Undirected Graph with Two vertices and Two edges between them. It would be a Euler Graph But Yet Not Simple Graph.

Comments

a connected graph which does not have more than 2 odd degree vertices either simple or multigraph is always have a euler path.

Answer 2

A closed walk containing every edge of a multigraph is called Eular circuit. And a multigraph containg eular circuit is called eular graph.

So graph should be simple not necessary.