Ad Invented by Sir William Rowan Hamilton in 1859 as a game

2. •

3. Introduction to
Hamiltonian

4. • AdInvented by Sir William Rowan
Hamilton in 1859 as a game
• Icosian Game = Hamilton's puzzle
• Finding Hamiltonian in
dodecahedron
• History

5. •
once and exactly once through every vertex of G (G can be digraph).
• Hamiltonian path is a path which passes once and exactly once through every vertex of G (G can be digraph).
• A graph is Hamiltonian iff a Hamiltonian cycle (HC) exists.

7. Hamiltonian Cycle |Backtracking

8. {
if (pos == V)
{
if ( graph[ path[pos-1] ][ path[0] ] == 1 )
return true;
else
return false;
}
for (int v = 1; v < V; v++)
{
if (isSafe(v, graph, path, pos))
{
path[pos] = v;
if (hamCycleUtil (graph, path, pos+1) == true)
return true;
path[pos] = -1;
}
}
return false;
}

10. • It is used in various fields such as Computer Graphics, electronic circuit design, mapping genomes, and operations research.
• A very simple application is planning bus route to pick up students (node->student, road-> edges, bus path-> Hamiltonian path)
• It is used in genome mapping to combine many tiny fragments of genetic code.

13. • The existence of the Hamilton's cycle (as in the tendering
scheme) will also allow the design of an automated test so that
once the data is entered and finally the test conditions are
created.
• So, designing tests and applications for Hamilton's existence in it
will save time when testing data transfer between states in an
application. If the test results prove positive, then the data is
moving correctly and there are no gaps or defects between
transition states.