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Discrete Mathematics. Tests with answers (25 jobs)
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Task 1
Question 1: What you need to ask (to draw or write) to strictly define a graph that is not a zero-graph?
1. Table football competitions
2. scrap curved line
3. A set of points and a set of lines connecting them
4. Draw a few overlapping lines
5. Put a few points and label them letters
Question 2. What is the number of edges of a complete graph ........?
Question 3. What are the graphs are isomorphic?
1. Graphs, images are overlaid
2. Graphs, which is the same number of edges
3. Graphs that have the same number of vertices
4. Counts, whose edges intersect only at the vertices
5. The graph with the same number of vertices (call it) and the same number of edges, and you can enumerate the top of each graph with numbers from 1 to, that if in one graph vertices connected by an edge with numbers and then in another box tops and also necessarily connected by an edge
Question 4. What is called planar graphs?
1. The graphs drawn on a flat surface
2. Graphs, all the edges of which are straight line segments
3. Graphs drawn by so that their edges intersect only at the vertices
4. Graphs depicting the streets of the city
5. The graphs that can be drawn so that their ribs will intersect only at the vertices
Question 5. Assume that the graph has 5 vertices of degrees 4, 1, 1, 3, 1. What is the number of edges of the graph?
1. 10
2. 8
3. 7
4. 5
5. 6
Task 2
Question 1. Consider the graph in Figure 13. Which of the following sequence of edges is an elementary chain?
1. ABCDEGBA
2. CEGAFED
3. GFECBAF
4. FAGBCDE
5. ECDEFG
Question 2. Consider the graph in Figure 13. Which of the following sequence of edges is a cycle?
1. AGEDCB
2. AFEDCEGA
3. AGEFGA
4. GBCDEGF
5. EGFEDCB
Question 3. Consider the five different graphs with the same number of vertices, labeled A, B, C, D, E. The following for each of these graphs is specified set of vertex degrees. Which of
Additional information
sets corresponding to the count, having chain having all its edges once?
1. (A) = 1, (B) = 3, (C) = 3, (D) = 3, (E) = 4
2. (A) = 2, (B) = 3, (C) = 1, (D) = 1, (E) = 3
3. (A) = 0, (B) = 3, (C) = 3, (D) = 3, (E) = 3
4. (A) = 1, (B) = 3, (C) = 1, (D) = 3, (E) = 2
5. (A) = 2, (B) = 3, (C) = 2, (D) = 1, (E) = 2
Question 4. What is called the Euler graph?
1. Count the amount of degrees of vertices is even
2. Count, where you can find a path through all the edges is at once
3. The graph whose edges correspond to Konigsberg bridges
4. Graphite having a cycle which contains all edges, and once every
5. Count, which does not contain the Euler line
Question 5: In what case the graph does not have the Euler line?
1. If the graph is an Euler
2. If the graph is connected
3. If the graph is not a cycle, having at one time all of his ribs
4. If the graph is connected and the degrees of all its vertices are even
5. In all the cases, the graph can have the Euler line
Activity 3
Question 1. What is a tree?
1. Count, containing at least one cycle.
2. The graph has a Hamiltonian line.
3. Count, given the incidence matrix.
4. Uniform graph with the number of edges, where - the number of vertices, - the degree of the graph.
5. A connected graph that contains no cycles.
Question 2. What is called the forest?
1. A lot of trees.
2. A graph formed by connecting the ribs of a number of trees.
3. Count the vertices having ribs.
4. The graph obtained by adding edges to a certain tree.
5. Count formed from the root of a tree by connecting the ribs with all end vertices.
Question 3. How many component comprises a forest of nodes and edges?
Question 4. If the count ...... vertices and edges, which is equal to its cyclomatic number?
Question 5: Under what conditions can establish a one-to-one correspondence between the edges and vertices of a connected graph incident?
1. The presence of a Hamiltonian line.
2. The absence of the Euler line.
3. Demands that the graph is a tree.
4. The graph should
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