Necessary and Sufficient Conditions for Euler Circuits and Paths

Necessary and Sufficient Conditions for Euler Circuits and Paths:

Necessary and Sufficient Conditions for Euler Circuits and Paths:

• If a connected multigraph has an Euler circuit, we can say that every vertex must have even degree.
• An Euler graph has been constructed if every edge has been used.
• The terminal vertices(beginning and ending vertex) must be same.

figure 3: Mohammed’s Scimitars

• The above graph is an Euler graph since it satisfies all the conditions to be an Euler graph.
• Here in graph, the dark spots are vertices and the line joined between vertices are called Euler line. The path a,b,d,g,h,j,i,k,g,f,d,c,b,e,i,f,e,a
• This circuit gives the way to draw scimitars without lifting the pencil or retracing part of the pictures.