Algorithm for Connectedness and Components:

The following algorithm checks the connectedness of graphs.

S$-1$ Set HGand component count c$=1$

$5-2$: Choose an arbitrary vertex v of G

$5-3$: Fuse all vertices in the neighbourhood $\backslash$overline$\{$N$\}[$v$]$ with v and call this vertex v$.$

$5-4$: If the number of vertices which are non$-$adjacent to v is the same as that before the fusion, then go to Step$-5.$ Otherwise, go to Step$-2.$ S$-5$: Delete the vertex v $($with all fused vertex$)$ from $/$ call this new graph H$.$

$5-6$: If If has any vertes left in it$,$ then let c$\backslash$leftarrow c$+1$ and go to Step$-2.$ Otherwise, go to Step$-7.$

S$-7$: Print each with its vertices. Stop.

Example $11\mathrm{.}1$ Consider the graph given$$in$$Figure$2$: