Math Problem Statement

Draw the graph with 3 vertices A, B, C, D & E such that the deg(A)=3,B is an odd vertex, deg(C)=2 and D and E are adjacent.

Solution

Here is the graph that satisfies the given conditions:

  • AA has degree 3.
  • BB has an odd degree.
  • CC has degree 2.
  • DD and EE are adjacent.

Would you like a breakdown of how each condition is met, or do you have any questions?

Further exploration questions:

  1. How do you calculate the total number of edges in a graph from vertex degrees?
  2. What are some properties of graphs with odd-degree vertices?
  3. Can the graph still satisfy the conditions if more edges are added?
  4. How would the graph change if DD and EE were not adjacent?
  5. What if BB's degree was specifically required to be 3 instead of just odd?

Tip: In graph theory, the sum of the degrees of all vertices is always twice the number of edges.

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Math Problem Analysis

Mathematical Concepts

Graph Theory
Vertex Degree
Adjacency in Graphs

Formulas

Sum of the degrees of all vertices = 2 × (number of edges)
Degree of a vertex = number of edges connected to the vertex

Theorems

Handshaking Lemma

Suitable Grade Level

Grades 9-12

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