This PowerPoint contains introduction of basic operations like subgraph, union of graph , complement of graph

1. Mr. S.L. Khairnar

3. Subgraph

4. A subgraph of a graph G = (V;E) is a graph
H = (W; F), where W⊆V and
F ⊆ E.
A subgraph H of G is a proper subgraph of
G if H ≠ G.

5. Note. if we remove one edge from G then H=G-{e} is also
a subgraph of G
Note. if we remove one vertex from G then H=G-{v} is also
a subgraph of G
Note. if we add one edge in G then G is a subgraph of H =
G + {e}
Note. if we add one vertex in G then G is a subgraph of H
= G + {v}

6. Union

8. Complement

9. It is denoted by 𝐺 . It is obtained from G by
using following rule
“e is an edge of 𝐺 if and only if e is not an
edge of G "

10. Representation of Graph

11. Adjacency Matrix Representation

13. Incidence Matrix Representation

15. Examples

21. Properties

22. Path of length n

24. Circuit

25. The path is a circuit if it begins and ends at the
same vertex, that is, if u = v, and has length
greater than zero.

26. Simple Path or Circuit

27. A path or circuit is simple if it does not contain the
same edge more than once.