Question
Download Solution PDFThe incident matrix of a graph is given below:
| 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 |
The corresponding graph is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- The no. of rows in an incident matrix determines the total no. of nodes present in a graph.
- The no. of columns in an incident matrix determines the total no. of branches present in a graph.
- The incoming arrow to a node is taken as -1.
- The outgoing arrow to a node is taken as +1.
Explanation:
| 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 |
Following are the results from the above incident matrix:
No. of rows = 4 = Total no. of nodes
No. of columns = 6 = Total no. of branches
Node 1: Three outgoing arrows
Node 2: Two incoming and one outgoing arrow
Node 3: One incoming and two outgoing arrows
Node 4: Three incoming arrows
All the above conditions are fulfilled by option 2.
Last updated on Jun 13, 2025
-> BPSC AE 2025 exam date has been revised. The exam will be conducted on July 17, 18 & 19 now.
-> Candidates who were facing technical issues while filling form can now fill the BPSC AE application form 2025 without any issue.
->BPSC AE age limit 2025 has been revised.
->BPSC AE application form 2025 was released on April 30. The last date to fill BPSC AE form 2025 was May 28.
->BPSC AE interview call letters released for Advt. 32/2024.
->BPSC AE notification 2025 has been released.
->A total of 1024 vacancies are announced through BPSC AE recruitment 2025
->The BPSC Exam Calendar 2025 has been released for the Assistant Engineer Recruitment.
-> The selection will be based on a written exam and evaluation of work experience.
-> Candidates with a graduation in the concerned engineering stream are eligible for this post.
-> To prepare for the exam solve BPSC AE Previous Year Papers. Also, attempt the BPSC AE Civil Mock Tests.