degree

                                                               DEGREE OF A GRAPH

                       Number of edges incident with a graph is called degree of a graph.

                                In this graph every vertex is labelled by its degree.An isolated vertex is having degree 0.

                                If the degree of every vertex is same that graph is called regular graph.eg.Kregular graph,Pregular graph.
This is a regular graph because each and every vertex is having degree 3.
                                                            Cycles and complete graphs are always regular graphs.

                                                           HANDSHAKING THEOREM


                                                             Sum of the degrees of all the vertices of a graph is twice the number of edges.This theorem is known as handshaking theorem.
                                                             In the example the sum of edges is 5 and the sum of degrees of the edges is 10.so sum of the degrees of all the vertices of this graph is twice the number of edges.

                                                                DEGREE SEQUENCE

                                                              It is a sequence of non-negative integers which would be the of vertices of some graph.



                                                                     GRAPH INVARIANTS

1. Number of vertices
2. Number of edges.
3. Degree sequence
4. Number of cycles
5.  Number of paths

                                                               COMPLEMENT OF A GRAPH

The complement of a graph with vertex set V denoted by G' is another graph with same vertex set V with the condition that 2 vertices are adjacent in G if and only if they are not adjacent  in G'

                                                The combination of a graph and its complement is a complete graph.