Question

True or False?

The following incidence matrix can be used to represent the graph. eg e8 e2 e6 ez e5 e1 e2 e3 e4 e5 e6 e7 e8e9 A5101000011 B 1 1 0 0 0 0 0 0 0 c011110000 D O 0 0 1 1 1 1 0 0 EL000001 1 1 1

Answer 1

Q) The above-mentioned incident matrix is representing the graph.

Ans) TRUE

Incident Matrix:

We can say that an incident matrix will tell about  the relationship between the vertices(nodes) and the edges(which connects the nodes)

Let's observe the above-undirected graph(with no directions from one node to another), Consider

1. Node A:

we have 4 edges connected with Node A to other nodes which are e1,e3,e8,e9

2. Node B:

We have 2 edges connected with Node B to other nodes namely e1,e2

3. Node C:

We have 4 edges connected with Node C to other nodes namely e2,e3,e4,e5

4. Node D:

We have 4 edges connected with Node D to other nodes which are e4,e5,e6,e7

5. Node E:

We have 4 edges connected from Node E to other nodes which are e6,e7,e8,e9

So, to construct an incidence matrix,

- Let's put the number of rows equal to the number of nodes in the graph which is 5 and the number of columns to the total number of edges connected across all the nodes which are 9

- Then check if there is a link between that particular node with that particular edge if exists put 1 else put 0

- Check with all other edges for all the nodes mentioned

- Put 0 for no link else put 1 if the connection exists between node and edge.

Hope this Helps!!!

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