Math Problem Statement
Determine the degree of each vertex of the graph and the total degree of the graph
Solution
To determine the degree of each vertex in a graph and the total degree of the graph, we need to understand a few key definitions:
- Degree of a vertex: The degree of a vertex is the number of edges connected to that vertex.
- Total degree of the graph: The total degree of the graph is the sum of the degrees of all vertices. This is also equal to twice the number of edges in the graph (since each edge contributes to the degree of two vertices).
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Math Problem Analysis
Mathematical Concepts
Graph Theory
Vertex Degree
Total Degree of a Graph
Formulas
Degree of a vertex v: deg(v) = Number of edges connected to v
Total degree of a graph: Sum of degrees of all vertices = 2 × Number of edges
Theorems
Handshake Theorem: The sum of the degrees of all vertices in a graph is equal to twice the number of edges
Suitable Grade Level
Grades 9-12