This document discusses paths and walks in graphs. It defines a path as a walk that does not repeat any vertices except possibly the first and last. It then defines an Eulerian path as one that uses each edge exactly once and a Hamiltonian path as one that visits each vertex once. The document also mentions that Leonhard Euler and William Rowan Hamilton contributed theories related to paths.

2. Path & Walk
• Path
– Path is a walk that does not include any vertex
twice, except that its first vertex might be the
same as its last
There are two Mathematician they given their
theory on path.
1) Leonhard Euler.
2) William Rowan Hamilton.

3. Path & Walk
• Eulerian Path
– A path in which every edge of the graph in present exactly
once.

4. Path & Walk

5. Path & Walk
• Hamiltonian Path
– A path in which every vertex of the graph is present once
and only once.