Tuesday, August 27, 2013

representation of graphs



                                             ADJACENCY MATRIX AND GRAPHS 

Any graphs can be represented as adjacency matrices without even drawing the vertices and edges.
6n-graph2.svg                                                                                 \begin{pmatrix} 1 & 1 & 0 & 0 & 1 & 0\\ 1 & 0 & 1 & 0 & 1 & 0\\ 0 & 1 & 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0 & 1 & 1\\ 1 & 1 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0\\ \end{pmatrix}



Here the graph itself is represented using the adjacency matrix.Vertices connected to each other by edges are denoted as 1 and otherwise 0.This matrix is enough to identify the graph.

                                                         INCIDENCE RELATION


                        \begin{pmatrix} 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ \end{pmatrix}



                               Entry of an incidence matrix is set to 1 if an edge incidence on a vertex otherwise it is set to zero.


                                                            ADJACENCY LIST

                          In this representation,every vertexes connected to a particular edge is plotted.











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