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Discrete Mathematics Graphs and Trees Please show all work. Suppose a graph has vertices of degrees...
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...
Topic: Discrete Mathematics and its Applications"
Chapter 10: Graph Terminology and Special Types of
Graphs,"
v(v - 1) u Variation on 10.2# 61. If a sim ple graph G h how many edges does G, the complement of G, have? 3. as v vertices and * -k edges. Answer: Explanaion:
A graph has 4 vertices of degrees 3, 3, 4, 4. (a) How many edges such a graph have? (b) Draw two non isomorphic such graphs. (c) Explain why there is no such simple graph
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
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...
Question 16. A maximal plane
graph is a plane graph G = (V, E) with n ≥ 3 vertices such that if
we join any two non-adjacent vertices in G, we obtain a non-plane
graph. (a) Draw a maximal plane graphs on six vertices. (b) Show
that a maximal plane graph on n points has 3n − 6 edges and 2n − 4
faces. (c) A triangulation of an n-gon is a plane graph whose
infinite face boundary is a...
Do in Computing Mathematics or Discrete
Mathematics
3. (8 pts) A graph is called planar if it can be drawn in the plane without any edges crossing. The Euler's formula states that v - etr = 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. (a) Find the maximum number of edges in G. (b) Find...
Discrete Math
Create a graph with 4 vertices of degrees 2, 2, 3, 3 or explain why no such graph exists. If the graph exists, draw the graph, label the vertices and edges. To answer the question in the box below, write the vertex set, the edge set, and the edge-endpoint function as shown on page 627 of the text. You can copy (Ctrl-C) and paste(Ctrl-V) the table to use in your answer if you like. Vertex set- Edge set...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...