Planar graph

Related BrainMass Solutions

• Prove that a planar graph of order n>=3 and size m is maximal planar if and only if m=3n-6

  104030 Prove that a planar graph of order for maximal planar 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?

• Planar Graph

  Theorem: If G is a planar (n,m) graph with n>=3, then m<=3n-6. A K5 graph is proven to be non-planar. Planar and non-planar graphs are analyzed.

• Outerplanar and Bipartite Graphs

  Hence, G+K_1 is planar. Proof of (2): As G+K_1 is planar, G+K_1 can be embedded in the plane. Note that the graph G+K_1 is the graph by adding an extra node v which is joined to every node in G.

• Prove : If G is a planar graph with n vertices, m edges and r regions , then n-m+r=1+k(G).

  104029 Planar graph with n vertices, m edges and r regions 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.

• Find values of p for which the faces of a planar p-regular graph are all triangles.

  30259 Find values of p for which the faces of a planar p-regular graph are all triangles. The faces of a planar p-regular graph are all triangles (that is each face has degree three).

• Petersen Graph

  So, it is clear that Petersen graph has as a subcontraction. Hence, it is non-planar. b) using the problem 1 show above part a) In problem 1, for planar (n,m)-graph G, we can get an upper bound B for m in terms of n and k.

• Outerplanar Graphs

  As H is a planar graph with p+1 vertices and p+q edges, by a known result (Theorem 6.3 on page 156, Graphs and Digraphs, third edition, G. Chartrand and L.

• Let T be a tree of order at least 4, and let e1, e2, e3 belong E(T^). Prove that T+e1 +e2+ e3 is planar.

  Prove that T+e1 +e2+ e3 is planar. Let T be a tree of order at least 4, and let e1, e2, e3 belong E(T^), T^ means Complement of T. Prove that T+e1 +e2+ e3 is planar. Please, draw the graph and explain it step by step.

• Nodes

  23479 Nodes - 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? See attachment please!