What is the maximum possible number of edges in a graph with n vertices if:
(a) the graph is simple?
(b) the graph is acyclic?
(c) the graph is planar?
Try to justify your answers. [Hint: first look at graphs with few vertices.]
Need a clear answer with good neat handwriting please.
What is the maximum possible number of edges in a graph with n vertices if: (a)...
solve with steps 1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number of edges of a simple connected graph G is at least n-1 where n is the number of vertices. Two graphs are isomorphic if they have the same number of vertices and 1) the same mumber of edges 1. (20 points)...
Let G be a directed graph on n vertices and maximum possible directed edges; assume that n ≥ 2. (a) How many directed edges are in G? Present such a digraph when n = 3 assuming vertices are 1, 2, and 3. You do not have to present a diagram, if you do not want to; you can simply present the directed edges as a set of ordered pairs. b) Is G, as specified in the problem, reflexive? Justify briefly....
2. What is the maximal possible number of edges in an undirected graph with n vertices. Explain your answer briefly.
Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
Question 9 3 pts What is the maximum possible number of edges in a directed graph with no self loops having 8 vertices? 0 56 O 28 0 64 256
Most Edges. Prove that if a graph with n vertices has chromatic number n, then the graph has n(n-1) edges. Divide. Let V = {1, 2, ..., 10} and E = {(x, y) : x, y € V, x + y, , and a divides y}. Draw the directed graph with vertices V and directed edges E.
Let G be a simple graph with 2n, n 2 vertices. Suppose there are at least n2 1 edges. Show that at least one triangle is formed. Hint: Check n 2 first and then use induction Let G be a simple graph with 2n, n 2 vertices. Suppose there are at least n2 1 edges. Show that at least one triangle is formed. Hint: Check n 2 first and then use induction
Assume that the graphs in this problem are simple undirected graphs A. The minimum possible vertex degree in a connected undirected graph of N vertices is: B. The maximum possible vertex degree in a connected undirected graph of N vertices is: C. The minimum possible vertex degree in a connected undirected graph of N vertices with all vertex degree being equal is: D. The number of edges in a completely connected undirected graph of N vertices is: E. Minimum possible...
2. If possible, draw a simple graph with 11 edges and all vertices are of degree 3. If no such graph exists, explain why.
Let G -(V, E) be a graph. The complementary graph G of G has vertex set V. Two vertices are adjacent in G if and only if they are not adjacent in G. (a) For each of the following graphs, describe its complementary graph: (i) Km,.ni (i) W Are the resulting graphs connected? Justify your answers. (b) Describe the graph GUG. (c) If G is a simple graph with 15 edges and G has 13 edges, how many vertices does...