Homework Answers
that we have a graph with vertices 1,2,3,4,5,6,7 and edges
(1,5), (2,5),(3,4),(3,5),(6,2),(7,1),(7,4). this graph and execute
the function mexset 1() to find the number of vertices in the
largest independent set of the graph.
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Suppose that we have a graph with vertices 1, 2, 3, 4, 5, 6, 7 and...
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 th...
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...
Choose the true statement. There exists a graph with 7 vertices of degree 1, 2, 2,...
Choose the true statement. There exists a graph with 7 vertices of degree 1, 2, 2, 3, 4, 4 and 5, respectively. the four other possible answers are false There exists a bipartite graph with 14 vertices and 13 edges. There exists a planar and connected graph with 5 vertices, 6 edges and 4 faces. There exists a graph with 5 vertices of degree 2, 3, 4, 5 and 6, respectively.
Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges...
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...
7. An independent set in a graph G is a subset S C V(G) of vertices...
7. An independent set in a graph G is a subset S C V(G) of vertices of G which are pairwise non-adjacent (i.e., such that there are no edges between any of the vertices in S). Let Q(G) denote the size of the largest independent set in G. Prove that for a graph G with n vertices, GX(G)n- a(G)+ 1.
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...
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...
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac,...
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac, af ca. bc. be.bf. cd, ce, de, df). Weights: w(ab) = 2 w(ac) = 5, w(af) = 10, w(ca) = 2. w(be) = 2. w(be) = 10, w(bf) = 11. w(cd)= 9. w(ce) = 7. w(de) = 2. w(df) = 2. a. Draw the Graph. This is a directed, weighted graph so you need to include arrows and weights. You can insert a pic...
3. Find a graph with the given set of properties or explain why no such graph...
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 stated. (a) tree, 7 vertices, total degree = 12. (b) connected, no multi-edges, 5 vertices, 11 edges. (c) tree, all vertices have degree <3, 6 leaves, 4 internal vertices. (d) connected, five vertices, all vertices have degree 3.
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...
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...
X) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k ...
COMP Discrete Structures: Please answer completely and
clearly.
(3).
(5).
x) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k possible colors to each of the vertices/edges of G so that adjacent vertices/edges have different colors. Draw pictures of each of the following (a) A 4-coloring of the edges of the Petersen graph. (b) A 3-coloring of the vertices of the Petersen graph. (e) A 2-coloring (d) A...
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...
Choose the true statement. There exists a graph with 7 vertices of degree 1, 2, 2, 3, 4, 4 and 5, respectively. the four other possible answers are false There exists a bipartite graph with 14 vertices and 13 edges. There exists a planar and connected graph with 5 vertices, 6 edges and 4 faces. There exists a graph with 5 vertices of degree 2, 3, 4, 5 and 6, respectively.
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...
7. An independent set in a graph G is a subset S C V(G) of vertices of G which are pairwise non-adjacent (i.e., such that there are no edges between any of the vertices in S). Let Q(G) denote the size of the largest independent set in G. Prove that for a graph G with n vertices, GX(G)n- a(G)+ 1.
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...
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac, af ca. bc. be.bf. cd, ce, de, df). Weights: w(ab) = 2 w(ac) = 5, w(af) = 10, w(ca) = 2. w(be) = 2. w(be) = 10, w(bf) = 11. w(cd)= 9. w(ce) = 7. w(de) = 2. w(df) = 2. a. Draw the Graph. This is a directed, weighted graph so you need to include arrows and weights. You can insert a pic...
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 stated. (a) tree, 7 vertices, total degree = 12. (b) connected, no multi-edges, 5 vertices, 11 edges. (c) tree, all vertices have degree <3, 6 leaves, 4 internal vertices. (d) connected, five vertices, all vertices have degree 3.
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...
COMP Discrete Structures: Please answer completely and
clearly.
(3).
(5).
x) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k possible colors to each of the vertices/edges of G so that adjacent vertices/edges have different colors. Draw pictures of each of the following (a) A 4-coloring of the edges of the Petersen graph. (b) A 3-coloring of the vertices of the Petersen graph. (e) A 2-coloring (d) A...
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