Does there exists a 4-regular graph with 6 vertices? If so, construct the graphs.
Understand the Problem
The question is asking if a 4-regular graph can exist with 6 vertices. A 4-regular graph means that each vertex has exactly 4 edges connected to it. To solve this, we need to check the properties of regular graphs and determine if it is possible with the given number of vertices.
Answer
Yes, a 4-regular graph with 6 vertices exists, for example, K_{3,3}.
Yes, there exists a 4-regular graph with 6 vertices. A well-known example is the complete bipartite graph K_{3,3}.
Answer for screen readers
Yes, there exists a 4-regular graph with 6 vertices. A well-known example is the complete bipartite graph K_{3,3}.
More Information
A 4-regular graph on 6 vertices ensures each vertex has exactly 4 connections. The complete bipartite graph K_{3,3} perfectly meets this criterion.
Tips
A common mistake is assuming such graphs cannot exist because not all combinations of vertex degrees seem directly feasible. Understanding bipartite graphs can help solve this.
Sources
- Does a graph with 6 vertices where each vertex degree is 4 - math.stackexchange.com
- 3Does there exists a 4regular graph on 6 vertices If so - studocu.com
AI-generated content may contain errors. Please verify critical information
