What is the sum of the degree of all vertices in a graph equal to?
Understand the Problem
The question relates to the properties of vertices in graph theory and discusses concepts such as pendant and isolated vertices, even and odd vertices, as well as the relationship between the degree of vertices and the number of edges in a graph. It specifically mentions the Handshaking theorem.
Answer
Twice the number of edges.
The sum of the degree of all vertices in a graph is equal to twice the number of edges.
Answer for screen readers
The sum of the degree of all vertices in a graph is equal to twice the number of edges.
More Information
This relationship in graph theory is derived from the fact that each edge connects to two vertices, effectively counted twice in the sum.
Tips
A common mistake is confusing vertex degrees with the number of edges directly.
Sources
- The web page with info on - Example Source - whitman.edu
- Proof that the sum of all degrees is equal to twice the number of edges - math.stackexchange.com
- Maths in a minute: Graphs and the degree sum formula - plus.maths.org
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