A graph consists of the collection of vertices and edges, where an edge is a connection between any two vertices.

We can make a graph by drawing some lines connecting edges, which are joined by vertices.**Graph Theory Basics:**

1. A directed graph which is generally denoted as G = (V, E) have a finite set V and a binary relation on V.

2. An undirected graph denoted as G = (V, E) has a finite set V and a set of multi-sets of two elements from V.

3. A graph is said to be complete if every pair of its distinct vertices is adjacent.

4.
The precise way to represent a graph is to say that it is made up of
the sets of vertices and the set of edges between these vertices.

5.
A sub graph H of a graph G = (V, E) is a sub-graph if H = (V', E')
satisfies V' is contained in V and E' is contained in E.

6. A simple path is a path with no vertex repeated.

7.
If there exists a path from every vertex to every other vertex in the
graph, then the graph is known as connected. A connected graph would
remain the same, if taken by any vertex, if the vertices are physical
and the edges as strings connecting them.

8. A cycle is a path,
(a way from a vertex back to itself), which is a simple path, but here,
the first and the last vertex are the same, that is the first vertex
meets the last after completing its cycle.

9. A graph with no
cycles is called a tree, and in a tree, there is only a single path
between any two nodes. A tree on N vertices has exactly N - 1 edges.

10. A sub graph that has all the vertices and forms a tree is known as a spanning tree of a graph.

11. A group of disconnected trees is called a forest.

12. The graphs which have a direction associated with each edge are known as directed graphs.

13. An edge ab in a directed graph can be used in a path which goes from a to b only not from b to a.

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1. a path,

2. a path which is not simple,

3. the number of connected components

4. and a cyclic path.

From the above graph, we can conclude that:

1. BA1FEG is a path from B to G.

2. BA1FEGA1C is not a simple path

3. It has three connected components as {I, H}, {J, K, L, M} and {A1, B, C, D, E, F, G}

4. The path A1FEGA1 is a cycle.

More topics in Graph Theory | |

Graph Coloring | Chromatic Number |

Edge Coloring | Trees |