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Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges...
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...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more tha...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
2 (a) Draw the graphs K5,2 and K5,3 using the standard arrangement. For example, K5,2 should have a row of 5 vertices above a row of 2 vertices, and the edges connect each vertex in the top row to ea...
2 (a) Draw the graphs K5,2 and K5,3 using the standard
arrangement.
For example, K5,2 should have a row of 5 vertices above a row of
2 vertices, and the edges connect each vertex in the top row to
each vertex in the bottom row.
(b) Draw K5,2 as a plane graph, i.e., with no edges
crossing.
(c) Complete the following table, recalling E is the number of
edges in a graph and V is the number of vertices. (Strictly...
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known...
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known three vertices have degree 3, one has degree 4, and another one has degree 7. Find the degree of the remaining vertex. (b) For each of the following graphs, determine if it is bipartite, complete, and/or a tree. Give a brief written or graphical justification for your answers (you may address multiple graphs at the same time). iii.
3. Find the number of vertices and edges for the line graph L(G) of a graph...
3. Find the number of vertices and edges for the line graph L(G) of a graph G with the degree sequence (di, d2, , dp). (Note that all edges in G incident to the same vertex are pairwise adjacent in L(G).)
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...
8. For each of the following, either draw a undirected graph satisfying the given criteria or...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
For a directed graph the in-degree of a vertex is the number of edges it has...
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
5. The in-degree of a vertex in a directed graph is the number of edges directed...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and...
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14
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...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
2 (a) Draw the graphs K5,2 and K5,3 using the standard
arrangement.
For example, K5,2 should have a row of 5 vertices above a row of
2 vertices, and the edges connect each vertex in the top row to
each vertex in the bottom row.
(b) Draw K5,2 as a plane graph, i.e., with no edges
crossing.
(c) Complete the following table, recalling E is the number of
edges in a graph and V is the number of vertices. (Strictly...
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known three vertices have degree 3, one has degree 4, and another one has degree 7. Find the degree of the remaining vertex. (b) For each of the following graphs, determine if it is bipartite, complete, and/or a tree. Give a brief written or graphical justification for your answers (you may address multiple graphs at the same time). iii.
3. Find the number of vertices and edges for the line graph L(G) of a graph G with the degree sequence (di, d2, , dp). (Note that all edges in G incident to the same vertex are pairwise adjacent in L(G).)
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...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14
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