---
title: "Influence graph for company board"
subject: "Discrete Structure"
chapter: 4
key: "semester_4/discrete_structure:influence-graph-company-board"
source: https://www.bctengineer.com/q/semester_4/discrete_structure/influence-graph-company-board
site: BCT Engineering
---

# Influence graph for company board

Discrete Structure · Chapter 4: Graph Theory

- Asked in: 2070 Magh, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/discrete_structure/influence-graph-company-board
- Whole chapter: https://www.bctengineer.com/md/semester_4/discrete_structure/chapter-4

## Question

Construct an influence graph for the board members of a company if the President can influence the Director of Research and Development, the Director of Marketing, and the Director of Operations; the Director of Research and Development can influence the Director of Operations; the Director of Marketing can influence the Director of Operations; and no one can influence, or be influenced by, the Chief Financial Officer.

## Short answer

Vertices: P, RD, M, O, CFO. Directed edges: P→RD, P→M, P→O; RD→O; M→O. CFO is isolated. The graph has 5 edges, P has out-degree 3, O has in-degree 3.

## Answer

An **influence graph** is a directed graph in which each person is a vertex and there is a directed edge from A to B if A can influence B.

**Vertices:** P (President), RD (Director of Research and Development), M (Director of Marketing), O (Director of Operations), CFO (Chief Financial Officer).

**Edges (influencer → influenced):**
- P → RD, P → M, P → O
- RD → O
- M → O
- CFO has no edges (isolated vertex).

```text
            P
         /  |  \
        v   |   v
       RD   |    M
         \  |   /
          v v  v
            O                CFO  (isolated)
```
(P has edges to RD, M and O; RD and M each have an edge to O.)

**Adjacency matrix** (row influences column):

| | P | RD | M | O | CFO |
|---|---|---|---|---|---|
| P | 0 | 1 | 1 | 1 | 0 |
| RD | 0 | 0 | 0 | 1 | 0 |
| M | 0 | 0 | 0 | 1 | 0 |
| O | 0 | 0 | 0 | 0 | 0 |
| CFO | 0 | 0 | 0 | 0 | 0 |

Reading it: the graph has 5 edges. P has out-degree 3 and in-degree 0, O has in-degree 3 (influenced by P, RD and M) and out-degree 0, and the CFO has in-degree and out-degree 0.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What kind of graph is an influence graph, and what does edge A -> B mean?
   A. Undirected; A and B know each other
   B. Directed; A can influence B
   C. Directed; B can influence A
   D. Weighted; A is paid by B
   Answer: B. Each person is a vertex and a directed edge points from influencer to influenced. (Key point: Graph type)

2. Which edge set is correct for the company?
   A. P->RD, P->M, P->O, RD->O, M->O
   B. RD->P, M->P, O->P, O->RD, O->M
   C. P->RD, P->M, RD->O, M->O, O->CFO
   D. P->CFO, RD->CFO, M->CFO, O->CFO, P->O
   Answer: A. President influences RD, M, O; RD and M each influence O. (Key point: Edges)

3. How is the Chief Financial Officer drawn?
   A. With an edge from P
   B. With an edge to O
   C. As a vertex with a loop
   D. As an isolated vertex with no edges
   Answer: D. No one influences or is influenced by the CFO, so degree 0 in both directions. (Key point: CFO)

4. What are the degrees of O in this graph?
   A. In-degree 3, out-degree 0
   B. In-degree 0, out-degree 3
   C. In-degree 2, out-degree 1
   D. In-degree 1, out-degree 2
   Answer: A. O is influenced by P, RD and M and influences nobody. (Key point: Degrees)

## Related in Discrete Structure

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- [DFA with no three consecutive 0's](https://www.bctengineer.com/question.md?key=semester_4%2Fdiscrete_structure%3Adfa-no-three-consecutive-zeros) — Discrete Structure, chapter 2

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