## Chapter 1

## Q. 1.P.29

Draw the incidence matrix of the following graph.

## Step-by-Step

## Verified Solution

In the incidence matrix column represents branches, while rows represent nodes. Therefore,

Note: In matrix A with n rows and b columns, an entry a_{i j} \text { in the } i^{\text {th }} \text { row and } j^{\text {th }} column has the following values:

a_{i j}=1, \text { if } j^{\text {th }} branch is incident to and oriented away from the i^{th} node.

a_{i j}=-1, \text { if } j^{\text {th }} branch is incident to and oriented towards i^{\text {th }} node.

a_{i j}=0 \text {, if } j^{\text {th }} branch is not incident to the i^{\text {th }} node.

Branches | ||||||

Nodes | a | b | c | d | e | f |

1 | 1 | 0 | 1 | 0 | 0 | 1 |

2 | -1 | -1 | 0 | 1 | 0 | 0 |

3 | 0 | 1 | 0 | 0 | 1 | -1 |

4 | 0 | 0 | -1 | -1 | -1 | 0 |