##### Distance Between Vertices and Connected Components of Graphs

If there is walk (and hence a path from u to vin given graph G).

Let

d_{G}(u,v)= min { k | u --- ^{k}-->v} be the distance between u and v.

Disconnected

d_{G}(u,v) =∞ by convention ,when thereis no walk

**Note:** A graph G is connected if d_{G}(u,v) <∞ for all u,v∈G and disconnected otherwise.

The maximal connected sub graphs of G areits connected components

**c(G)**=# of connected component of G

here c(G) is 2.

what maximality condition mean is ?

Maximality condition means that a sub graph H ⊆ G is a connected sub graph and for any w ∈ V(G) w ∉ H

then G[V(H) ∪{w}] is disconnected.