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-An undirected graph is called complete if every vertex shares an edge with every other vertex. Draw a complete graph on five vertices. How many edges does it have?

-An undirected graph is called complete if every vertex shares an edge with every other vertex. Draw a complete graph on five vertices. How many edges does it have?

Advanced Engineering Mathematics
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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Exercises 2.1 1. Consider the following undirected graph. (a) How many edges are there in this graph? (b) Give the degree of each vertex. (c) Do these numbers agree with Euler's first observation? 2. Consider the following directed graph. 4 C (a) Give the indegree of each vertex. (b) Give the outdegree of each vertex. (c) Compute the sum of the indegrees and the sum of the outdegrees. What do you notice? 3. A circuit is simple if it has no repeated edges. Draw a connected, undirected graph with seven vertices and no simple circuits. How many edges does it have? 4. Draw an undirected graph with six vertices, each of degree 3, such that the graph is: (a) Connected. (b) Not connected. 5. A graph is called simple if it has no multiple edges or loops. (The graphs in Figures 2.3, 2.4, and 2.5 are simple, but the graphs in Example 2.1 and Figure 2.2 are not simple.) Draw five different connected, simple undirected graphs with four vertices. 6. An undirected graph is called complete if every vertex shares an edge with every other vertex. Draw a complete graph on five vertices. How many edges does it have?
Transcribed Image Text:Exercises 2.1 1. Consider the following undirected graph. (a) How many edges are there in this graph? (b) Give the degree of each vertex. (c) Do these numbers agree with Euler's first observation? 2. Consider the following directed graph. 4 C (a) Give the indegree of each vertex. (b) Give the outdegree of each vertex. (c) Compute the sum of the indegrees and the sum of the outdegrees. What do you notice? 3. A circuit is simple if it has no repeated edges. Draw a connected, undirected graph with seven vertices and no simple circuits. How many edges does it have? 4. Draw an undirected graph with six vertices, each of degree 3, such that the graph is: (a) Connected. (b) Not connected. 5. A graph is called simple if it has no multiple edges or loops. (The graphs in Figures 2.3, 2.4, and 2.5 are simple, but the graphs in Example 2.1 and Figure 2.2 are not simple.) Draw five different connected, simple undirected graphs with four vertices. 6. An undirected graph is called complete if every vertex shares an edge with every other vertex. Draw a complete graph on five vertices. How many edges does it have?
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