A graph G,consists of two sets V and E. V is a finite non-empty set of vertices.E is a set of pairs of vertices,these pairs are called as edges V(G) and E(G) will represent the sets of vertices and edges of graph G.

**Undirected graph** - It is a graph with V vertices and
E edges where E edges are undirected.In undirected graph, each edge
which is present between the vertices Vi and Vj,is represented by using
a pair of round vertices (Vi,Vj).

**Directed graph** - It is a graph with V vertices and
E edges where E edges are directed.In directed graph,if Vi and Vj nodes
having an edge.than it is represented by a pair of triangular brackets
Vi,Vj.

**Simple graph** - It is a graph, in which each edge occurs
only once.

**Multiple graph** - It is a graph, in which each edge
may occur multiple times.

**Complete graph** - A graph with maximum possible edges
is called as complete graph.

**Incident edge** - If (V1,V2) is an edge between the
vertices V1 and V2, then it is incident on the vertices V1 and V2.

**Adjacent Vertices** - If (V1,V2) is an edge , then the
vertices V1 and V2 are said to be the adjacent vertices.

**Path **- A path from vertex Vp to Vq in graph G is a
sequence of vertices Vp,Vi1,Vi2----Vin,Vq such that (Vp,Vi1),(Vi1,Vi2)----(Vin,Vq)
are the edges in E(G).

**Path Length** - It is the number of edges on it.

**Connected Vertices** - In an undirected graph G, two
vertices V1 and V2 are said to be connected if there is a path in G
from V1 to V2

For eg,V1--P--Q--R--S--V2

In a directed graph G, two vertices V1 and V2 are said to be connected if a directed path is there in G from V1 to V2.

Note - The adjacent nodes are always the connected nodes but the connected vertices or nodes may not be the adjacent nodes. This is because the adjacent nodes do not allow a path containing many nodes.

For eg, V1---V2 Adjacent and connected

V1--P--Q--V2 Connected and not adjacent

**Connected graph** - An undirected graph is said to be
connected if for every pair of distinct vertices Vi,Vj in V(G) there
is a path from Vi to Vj in G.

**Connected component** - A connected component or simply
a component of a undirected graph is a maximal connected subgraph.

**Strongly connected directed graph** - A directed graph
G is said to be strongly connected if for every pair of distinct vertices
Vi,Vj in V(G) there is a directed path from Vi to Vj and also from Vj
to Vi.

**Vertex degree** - The degree of a vertex is the number
of edges incident to that vertex.

Sr.No. | Programe Name |

1 | Adjacency matrix method |

2 | Adjacency List |

3 | Depth First Search Method |