Question

30. a) Show if G is a connected planar simple graph with v vertices and e...

30. a) Show if G is a connected planar simple graph with v vertices and e edges with v ≥ 3 then e ≤ 3v−6.

b) Further show if G has no circuits of length 3 then e ≤ 2v−4.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

PLEASE LIKE IT RAISE YOUR THUMBS UP

IF YOU ARE HAVING ANY DOUBT FEEL FREE TO ASK IN COMMENT SECTION

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
show that any simple, connected graph with 31 edges and 12 vertices is not planar.
show that any simple, connected graph with 31 edges and 12 vertices is not planar.
A graph is called planar if it can be drawn in the plane without any edges...
A graph is called planar if it can be drawn in the plane without any edges crossing. The Euler’s formula states that v − e + r = 2, where v,e, and r are the numbers of vertices, edges, and regions in a planar graph, respectively. For the following problems, let G be a planar simple graph with 8 vertices. Find the maximum number of edges in G. Find the maximum number of edges in G, if G has no...
Let G = (V,E) be a graph with n vertices and e edges. Show that the...
Let G = (V,E) be a graph with n vertices and e edges. Show that the following statements are equivalent: 1. G is a tree 2. G is connected and n = e + 1 3. G has no cycles and n = e + 1 4. If u and v are vertices in G, then there exists a unique path connecting u and v.
Suppose we are going to color the vertices of a connected planar simple graph such that...
Suppose we are going to color the vertices of a connected planar simple graph such that no two adjacent vertices are with the same color. (a) Prove that if G is a connected planar simple graph, then G has a vertex of degree at most five. (b) Prove that every connected planar simple graph can be colored using six or fewer colors.
A spanning tree of connected graph G = (V, E) is an acyclic connected subgraph (V,...
A spanning tree of connected graph G = (V, E) is an acyclic connected subgraph (V, E0 ) with the same vertices as G. Show that every connected graph G = (V, E) contains a spanning tree. (It is the connected subgraph (V, E0 ) with the smallest number of edges.)
Let G be a connected planar graph with 3 or more vertices which is drawn in...
Let G be a connected planar graph with 3 or more vertices which is drawn in the plane. Let ν, ε, and f be as usual. a) Use P i fi = 2ε to show that f ≤ 2ε 3 . b) Prove that ε ≤ 3ν − 6. c) Use b) to show that K5 is not planar.
If a connected 3-regular planar graph G has 18 vertices, then the number of faces of...
If a connected 3-regular planar graph G has 18 vertices, then the number of faces of a planar representation of G is..........
Let there be planar graph G with 12 vertices where every vertices may or may not...
Let there be planar graph G with 12 vertices where every vertices may or may not be connected by an edge. The edges in G cannot intersect. What is the maximum number of edges in G. Draw an example of G. What do you notice about the faces and the maximum number of edges?
Let G be a connected simple graph with n vertices and m edges. Prove that G...
Let G be a connected simple graph with n vertices and m edges. Prove that G contains at least m−n+ 1 different subgraphs which are polygons (=circuits). Note: Different polygons can have edges in common. For instance, a square with a diagonal edge has three different polygons (the square and two different triangles) even though every pair of polygons have at least one edge in common.
Suppose that a connected planar graph has eight vertices each of degree 3 then how many...
Suppose that a connected planar graph has eight vertices each of degree 3 then how many regions does it have?And suppose that a polyhedron has 12 triangular faces then determine the number of edges and vertices.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT