Connectivity Graph Theory in Computer Applications

1. Present by: Abdul Ahad Abro
1
Graph Theory in Computer Applications
Computer Engineering Department, Ege University, Turkey
October 26-2017
Connectivity

2. Connectivity Bağlantı
The message can be sent between two computers using intermediate links
can be studied with a graph model. Problems of efficiently planning routes for
mail delivery, garbage pickup, diagnostics in computer networks and so on
can be solved using models that that involve paths in graphs .
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Fig: 01 Connectivity

3. Path is a sequence of edges that begins at a vertex of a graph and travels from vertex to
vertex along edges of the graph.
Vertices cannot repeat. Edges cannot repeat (Open) .
Path of length 4 - 1,2,3,4,6
A closed path is called Cycle. (a-b-c-d-a)
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Paths Yollar
Fig: 02 Path

4. A Path in which edges/nodes can be repeated.
a-b-d-a-b-c
Walk of length 5 - 1,2,5,2,3,4
Vertices may repeat. Edges may repeat (Closed or Open)
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Walk Yürüme
Fig: 03 Walk

5. Trail: iz
If all the edges (but not necessarily all the vertices) of a walk are different, then the walk is
called a trail.
No Edge can be repeat.
a-b-c-d-e-b-d
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Fig: 04 Trail

6. A circuit is a path that begins and end at the same vertex.
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In this graph a,d,c,f,e is a simple path of length 4, because {a,d}, {d,c}, {c,f} and {f,e} are all
edges. However d,e,c,a is not a path because {e,c} is not an edge. Where as {b,c}, {c,f}, {f,e}
and {e,b} are edges and this path begins and ends at b.
Circuit
Fig: 05 Simple Graph

7. 7
When does a computer network have the property that every pair of
computers can share information, if messages can be sent through one or
more intermediate computers? When a graph is used to represent this
computer network, where vertices represent the computers and edges
represent the communication links.
Connectedness in Undirected Graphs

8. The graph H and its connected components H1, H2, H3
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Any two computers in the network can communicate if and only if the graph of this
network is connected .
Fig: 06 Connected Components

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A cut-edge or cut-vertex of a graph is an edge or vertex whose deletion
increases the number of components.
Cut Edge or Cut Vertex
Fig: 07 Cut Edge or Cut Vertex

10. 10
A directed graph is said to be strongly connected only if every pair of distinct
vertices are connected.
In a weakly connected graph the nodes cannot be visited by a single path.
Strongly / Weakly Connected Directed Graphs
Fig: 08 strong and weakly connected graph

11. 11
Two graphs are isomorphic if and only if after recording the vertices their adjacency
matrices are the same.
Isomorphism
Isomorphic Not Isomorphic
Fig: 09 Isomorphism

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