Mathematics Homework Solutions
#23479
Graphs and Their Representations
If all the nodes of a simple, connected, planar graph have degree 4 and the number of arcs is 12, into how many regions does it divide the plane?
This shows how to work with nodes of a simple connected graph.
What is this?
By OTA - Overall OTA Rating
Changping Wang, MA - 4.9/5
Purchase Cost Now
$2.19 CAD (was ~$7.98)
Included in Download
- Plain text response
- Attached file(s):
- planar-graph.doc
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Planar Graph - Prove that the complete graph K5 is nonplanar.
- Prove that a planar graph of order n>=3 and size m is maximal planar if and only if m=3n-6. - Prove that a planar graph of order n>=3 and size m is maximal planar if and only if m=3n-6 What does maximal planar graph mean?
- Maximal planar graph - Prove that there exists only one 4-regular maximal planar graph. Hint: there is a proof on two lines. If you don't find it, then it may take a page or two, but no more.
- Give an example of planar graph that contains no vertex of degree less than 5 . - Give an example of planar graph that contains no vertex of degree less than 5 .
- Prove : If G is a planar graph with n vertices, m edges and r regions , then n-m+r=1+k(G). - Prove : If G is a planar graph with n vertices, m edges and r regions , then n-m+r=1+k(G). K(G) is the number of component. Can you explain what is n-cube Qn and explain it step by step?
