The document discusses graphs and their representations. It defines a graph as consisting of nodes and edges that connect pairs of nodes. Adjacency lists are described as the standard way to represent graphs, with each edge appearing in two lists doubling the space. A topological sort orders the vertices in a directed acyclic graph such that if there is an edge from vertex v to w, then v appears before w in the ordering. It is not possible to perform a topological sort if the graph contains a cycle. Pseudocode for a topological sort algorithm is provided.

1. M.PREETHA
M.Sc(information technology)
NADAR SARASWATHI COLLEGE OF ARTS
&SCIENCEech)

2.  A graph is an non-linear data
structure consisting of nodes and
edges.
 The nodes are sometime vertices and
edges are lines or arcs connect any
two nodes in the graph.
 A graph consists of a finite set of
vertices and set of edges which
connect pair of nodes.

3.  Adjacency lists are the standard way to
represent graphs.
 Edge (u,v) in appears in two list, the space
essentially doubles.
 The vertices have name which are unknown at
compile time.
 To create a new vertex object and insert the
name and vertex object into hash table.

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5.  A topological sort is an ordering of vertices in
directed acyclic graph.
 A directed edge ( v,w) indicates that course v
must be completed .
 Topological ordering is not possible if the
graph has a cyclic for two vertices v & w on
the cycle.
 V precedes w and w precedes v.

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2
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5
6
7
2
4
6
6
4
6
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7
3
3

7. CAP37
00
MAD31
04
COP34
00
COP32
12
COP45
55
MAD33
05
MAD35
12
COP35
30
CDA41
01
CDA44
00
COP45
40
COP56
21
CIS461
0
COP[46
10
COP42
25
DP110

8. V4
V1 V2
V8 V5
V6 V7

9. void graph::topsort()
{
Vertex v, w;
For (int counter=0;counter<NUM_VERTICES;counter++)
{
V=findNewVertexOfDegreeZero();
If (v==NOT_A_VERTEX)
Throw cyclefound()
v.topnum=counter;
For each w adjacent to v
w.indegree--;
}
}