**Exercise 16: Graph Drawing**Draw the following graphs:a) \( K_4 \)b) \( K_5 \)c) \( K_6 \)d) \( K_{1,3} \)e) \( K_{2,2} \)f) \( K_{3,3} \)g) \( P_4 \)h) \( C_3 \)i) \( C_4 \)---**Explanation:**- **\( K_n \):** Complete graph with \( n \) vertices. Each pair of distinct vertices is connected by a unique edge.- **\( K_{m,n} \):** Complete bipartite graph where vertices are divided into two disjoint sets with \( m \) and \( n \) vertices. Each vertex from the first set is connected to every vertex in the second set.- **\( P_n \):** Path graph with \( n \) vertices arranged in a single path.- **\( C_n \):** Cycle graph with \( n \) vertices arranged in a closed loop. Draw the vertices and edges accordingly to illustrate these types of graphs.

Answered: 1O Draw the f llowing graphs:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Exercise 16: Graph Drawing**

Draw the following graphs:

a) \( K_4 \)

b) \( K_5 \)

c) \( K_6 \)

d) \( K_{1,3} \)

e) \( K_{2,2} \)

f) \( K_{3,3} \)

g) \( P_4 \)

h) \( C_3 \)

i) \( C_4 \)

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**Explanation:**

- **\( K_n \):** Complete graph with \( n \) vertices. Each pair of distinct vertices is connected by a unique edge.

- **\( K_{m,n} \):** Complete bipartite graph where vertices are divided into two disjoint sets with \( m \) and \( n \) vertices. Each vertex from the first set is connected to every vertex in the second set.

- **\( P_n \):** Path graph with \( n \) vertices arranged in a single path.

- **\( C_n \):** Cycle graph with \( n \) vertices arranged in a closed loop.

Draw the vertices and edges accordingly to illustrate these types of graphs.

Expert Solution

Step 1

In the given question , concept of graph theory is used.

Graph Theory

The branch of mathematics concerned with networks of points connected by lines is thought as graph theory. The term graph in graph theory doesn't check with data charts as line graphs or bar graphs. Instead, it refers to a collection of vertices (often called as points or nodes) and edges (also referred as lines) that connect the vertices.