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Topological Sort ?
-it   is ordering of vertices in a directed acyclic group .

If its path vi to vj then vj appears after vi in the ordering

 Topological ordering is not possible if the graph has acyclic ?.


      E.g:         v1                    v2



         v3                   v4
                                                       v5



                    v6                        v7
Algorithm for topologies :

    โ€ข    Create an array of length equal to the number of vertices.

โ€ข While the number of vertices is greater than 0, repeat:
.



    :โ€ข   Find a vertex with no incoming edges (โ€œno prerequisitesโ€).
    .


    โ€ข Put this vertex in the array.

    .โ€ขNote that this destructively updates a graph; often this is a
    bad idea, so make a copy of the graph first and do
    topological sort on the copy.
Topological Sort Algorithm
    The Topological sort algorithm is:
int topologicalOrderTraversal( ){
    int numVisitedVertices = 0;
    while(there are more vertices to be visited){
         if(there is no vertex with in-degree 0)
               break;
         else{
         select a vertex v that has in-degree 0;
         visit v;
         numVisitedVertices++;
         delete v and all its emanating edges;
       }
    }

     return numVisitedVertices;
}
Just we take this example 4 solve topological graph




      Here a=0 because in degree is 4 โ€˜aโ€™
Graph 1
vertex   A   B   C   D   E   F   G   H

A        0   1   1   0   1   0   0   0

B        0   0   0   0   0   1   0   0

C        0   0   0   1   0   1   1   0

D        0   1   0   0   1   0   0   1

E        0   0   0   0   0   1   0   0

F        0   0   0   0   0   0   0   1

G        0   0   0   0   1   0   0   1

h        0   0   0   0   0   0   0   0

Sum      0   2   1   1   3   3   1   3
of
colum
โ€ข Overview
โ€“ Terms
โ€ข Topics
โ€“ Ethernet-Standard
โ€“ Network topologies
โ€ข Bus topology
โ€ข Ring topology
โ€ข Star topology
โ€ข Fully connected topology
โ€ข Mesh topology
โ€“ IPv4 & IPv6
โ€ข Prototype of the Ethernet Standard
โ€ข Characteristics:
โ€“ A central cable (coaxial cable)
โ€“ Lines to the attached stations
โ€“ Decentralized structure (stations with equal standing)
โ€“ All attached stations are affected by disturbance at the central
cable
RING Topology
โ€ข One token "moves" in the circle (Ring
structure of the network)
โ€ข If the token is "free", then the station
can attach a network package



                  RING TYPE
Data structure

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Data structure

  • 1.
  • 2. Topological Sort ? -it is ordering of vertices in a directed acyclic group . If its path vi to vj then vj appears after vi in the ordering Topological ordering is not possible if the graph has acyclic ?. E.g: v1 v2 v3 v4 v5 v6 v7
  • 3. Algorithm for topologies : โ€ข Create an array of length equal to the number of vertices. โ€ข While the number of vertices is greater than 0, repeat: . :โ€ข Find a vertex with no incoming edges (โ€œno prerequisitesโ€). . โ€ข Put this vertex in the array. .โ€ขNote that this destructively updates a graph; often this is a bad idea, so make a copy of the graph first and do topological sort on the copy.
  • 4. Topological Sort Algorithm The Topological sort algorithm is: int topologicalOrderTraversal( ){ int numVisitedVertices = 0; while(there are more vertices to be visited){ if(there is no vertex with in-degree 0) break; else{ select a vertex v that has in-degree 0; visit v; numVisitedVertices++; delete v and all its emanating edges; } } return numVisitedVertices; }
  • 5. Just we take this example 4 solve topological graph Here a=0 because in degree is 4 โ€˜aโ€™
  • 6. Graph 1 vertex A B C D E F G H A 0 1 1 0 1 0 0 0 B 0 0 0 0 0 1 0 0 C 0 0 0 1 0 1 1 0 D 0 1 0 0 1 0 0 1 E 0 0 0 0 0 1 0 0 F 0 0 0 0 0 0 0 1 G 0 0 0 0 1 0 0 1 h 0 0 0 0 0 0 0 0 Sum 0 2 1 1 3 3 1 3 of colum
  • 7.
  • 8.
  • 9. โ€ข Overview โ€“ Terms โ€ข Topics โ€“ Ethernet-Standard โ€“ Network topologies โ€ข Bus topology โ€ข Ring topology โ€ข Star topology โ€ข Fully connected topology โ€ข Mesh topology โ€“ IPv4 & IPv6
  • 10. โ€ข Prototype of the Ethernet Standard โ€ข Characteristics: โ€“ A central cable (coaxial cable) โ€“ Lines to the attached stations โ€“ Decentralized structure (stations with equal standing) โ€“ All attached stations are affected by disturbance at the central cable
  • 11. RING Topology โ€ข One token "moves" in the circle (Ring structure of the network) โ€ข If the token is "free", then the station can attach a network package RING TYPE
  ็ฟป่ฏ‘๏ผš