Consider two graphs G and H. Graph G is a complete graph with 5 vertices; Graph H is a 2-regular graph with 10 vertices. How many edges are there in total between the two graphs?
Consider two graphs G and H. Graph G is a complete graph with 5 vertices; Graph H is a 2-regular graph with 10 vertices. How many edges are there in total between the two graphs?
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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![**Problem Statement:**
Consider two graphs G and H. Graph G is a complete graph with 5 vertices; Graph H is a 2-regular graph with 10 vertices. How many edges are there in total between the two graphs?
**Explanation:**
A complete graph with \( n \) vertices means every pair of distinct vertices is connected by a unique edge. Therefore, the number of edges in Graph G, which is complete with 5 vertices, can be calculated using the formula:
\[
\frac{n(n-1)}{2} = \frac{5 \times (5-1)}{2} = 10 \text{ edges}
\]
A 2-regular graph with 10 vertices means each vertex has exactly 2 connections, forming a cycle or disjoint cycles. Since each vertex connects to 2 others, the total number of edges is:
\[
\frac{n \times k}{2} = \frac{10 \times 2}{2} = 10 \text{ edges}
\]
**Total Edges:**
Adding the edges from both graphs, the total number of edges is:
\[
10 + 10 = 20 \text{ edges}
\]
**Answer Box:**
\[ \text{Total edges: } \_\_\_\_\_ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff60bf7ae-3e0a-47f1-9493-b686204b7388%2F356ae59d-ab87-4bba-bbaa-b0ba6e71ebbe%2F4pd8f8_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider two graphs G and H. Graph G is a complete graph with 5 vertices; Graph H is a 2-regular graph with 10 vertices. How many edges are there in total between the two graphs?
**Explanation:**
A complete graph with \( n \) vertices means every pair of distinct vertices is connected by a unique edge. Therefore, the number of edges in Graph G, which is complete with 5 vertices, can be calculated using the formula:
\[
\frac{n(n-1)}{2} = \frac{5 \times (5-1)}{2} = 10 \text{ edges}
\]
A 2-regular graph with 10 vertices means each vertex has exactly 2 connections, forming a cycle or disjoint cycles. Since each vertex connects to 2 others, the total number of edges is:
\[
\frac{n \times k}{2} = \frac{10 \times 2}{2} = 10 \text{ edges}
\]
**Total Edges:**
Adding the edges from both graphs, the total number of edges is:
\[
10 + 10 = 20 \text{ edges}
\]
**Answer Box:**
\[ \text{Total edges: } \_\_\_\_\_ \]
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