(I guess, readers might misguided by my original post, So I modify it)
If I have an undirected graph, Could you please help me to describe
- Decomposing a undirected graph into cycles
- Cycle breaking into 2 sections (via any 2 graph edges) and make 2 directed path graphs
- Obtainig big cycle by getting union of the cycles through the removal of common sharing edges
with mathematical notation (according to graph theory) Please help me.