1. The vertex set and the edge set are finite sets in a a) finite graph b) bipartite graph c) infinite graph d) connected graph

Q: The number of edges in a graph with 10 vertices each of degree 5 is

A: A graph G is a pair (V,E), where V is a finite set of vertices and E a finite set of edges. We can…

Q: 1. Show that the complement of a complete bipartite graph is the disjoint union of two complete…

A: We have to show that complement of a complete bipartite graph is the disjoint union of two complete…

Q: 1. In a complete graph with 5 vertices, how many triangles are there? (Remember: a triangle has 3…

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Q: Can the following graphs drawn in plane without edge crossings? a

A: Given: Graphs, To determine: Whether the given graphs can be drawn without crossing.

Q: If G is connected simple graph has 4 vertices with degree 3 and 2 vertices with degree 1. How many…

A: See the detailed solution below.

Q: Can you create a graph that has the following characteristics: a. Six vertices, five edges, not a…

A: a Six vertices ,five edges not a true

Q: 1. Suppose G is a planar graph with four faces of lengths 3, 4, 5, 6. How many edges are there in G?

A: Answer :-  a). Suppose G is a planar graph with faces of length 3, 4, 5, 6. How many edges are there…

Q: How many different labelled graphs are there on the vertex set [n]? Justify your claim.

A: Given Vertex set n Let vertex V=1, 2, 3, ........., n Each graph G with a vertex V is determined by…

Q: Let G be simple connected planar graph. If G has 8 vertices and 11 edges, in how many regions will…

A: Euler formula for planar graph: Let G be a connected planar graph, and let n, e and f denote,…

Q: If a graph has five vertices of degree 7 and eleven vertices of degree 3, and no other vertices, how…

A: according to question,  given graph has five vertices of degree 7 and eleven vertices of degree 3…

Q: Construct a bipartite graph with vertices R, S, T, U, V, W that is a tree. What is the edge set?…

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Q: 4. Find the number of edges in a circulant graph C'irc[n, k]. In mathematica you can explore these…

A: In circulant graph Circ n,k total number of vertices are n. And connectivity of the graph is k.

Q: Suppose a connected planar graph G has 27 vertices. How many edges must G have if there are 16…

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Q: If a planar drawing of a graph has 13 edges and 4 vertices, faces

A: Given a Planar Graph: Edges = 13 Vertices = 4 Faces = ? Planar Graphs: When any connected graph can…

Q: 37. Consider Graph A and B are isomorphic. If vertex E of Graph A corresponds to vertex 2 in Graph…

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Q: Let K, be the complete graph on n vertices. a) Draw Kn for n = 1, 2, 3, 4, 5. For each, how many…

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Q: The number of edges in a graph with 12 vertices each of degree 6 is O 72 O 1 O 12 O 36

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Q: Suppose we are told that a connected graph cuts the plane into 211 regions. How many more edges than…

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Q: (a) Prove that if a connected planar graph has 13 vertices and 12 edges then it must be a tree. (b)…

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Q: 27) A graph with an Euler circuit A) must be connected and every vertex must have odd degree. B)…

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Q: 11. Draw a graph with five vertices that is connected and draw a graph with five vertices that is…

A: The connected graphs with five vertices: A graph is called connected if there is a path between…

Q: 4) Which of the graphs has an Euler path but no Euler circuit?

A: 4. a) Given graph is  We observe that  degree of vertex A, i.e. d(A)=2, d(B)=4, d(C)=2, d(D)=3,…

Q: QUESTION 14 Total number of edges of a complete graph which has 9 vertices is 36 edges None 12 edges…

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Q: Construct a graph with vertices P, Q, R, S, T, U that has an Euler circuit and the degree of T is 4.…

A: We know that, Euler Circuit:  A circuit that uses every edge exactly once is called Euler Circuit.

Q: The number of edges in a graph with 10 vertices each of degree 7 is O 35 O 14 O 70

A: Given that  Number of vertices of the given graph=10 Degree of each vertices=7 To find Number of…

Q: Construct a bipartite graph with vertices I, J, K, L, M, N that is a tree. What is the edge set?…

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Q: Construct a bipartite graph with vertices T,U, V, W, X that is a tree. What is the edge set?…

A: A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets U…

Q: The number of edges in a graph with 8 vertices each of degree 5 is 10 O 20 O 7 O 40

A: We have to determine the number of edges in the graph with 8 vertices of degreee 5 .

Q: 17. List all the vertices that are adjacent to vertex A.

A: This question is related to graph and figures, we will solve it using given information.

Q: Given an acyclic graph G = (V, E) return the longest path from two connected vertices: u, v. Prove…

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Q: Imagine a very large connected graph that has 400 odd vertices and no even vertices. Does an Euler…

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Q: (a) which edges are incident on v,? (b) Which vertices are adjacent to v,? (c) which edges are…

A: Given: The graph

Q: If a graph has 5 vertices then 'By the Handshaking Theorem', each vertex can have degree 9. True…

A: Given: Statement: If a graph has 5 vertices then by handshaking theorem, each vertex can have degree…

Q: The number of edges in a graph with 11 vertices each of degree 4 is 44 O 22 O 8 O 10

A: Graph - number of edges

Q: A path that uses each edge of a connected graph once and ends at the starting vertex is called 1…

A: A path that uses each edge of a connected grapg once and ends at the same starting vertex is called…

Q: 17. Determine whether the given (a) directed graph and (b) undirected graph have a Euler circuit…

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Q: 2. Draw three different graph that has a Euler Circuit. (minimum of 5 vertices)

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Q: Show that every simple planar graph with n vertices, where n ≥ 3, is a subgraph generating a…

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Q: The number of edges in a graph with 8 vertices each of degree 7 is O 7 O 56 28 O 14

A: We have to solve given problem:

Q: How many non-isomorphic simple graphs edges? are there with four vertices and 3

A: Detailed explanation mentioned below

Q: 11. Determine if the following graph is bipartite graph. If it is, show how to divide its vertices…

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Q: 2) Find, with a proof, the number of distinct graphs with vertex set [n].

A: 2) The number of distinct graphs of vertex set for given n should be found. Let us take n=3.…

Q: et B

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Q: By duplicating only 2 edges, Eulerize the following graph:

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Q: 2. Draw a connected graph with five vertices in which one vertex has degree three, one vertex has…

A: Graph theory: draw the graph using vertex Degree

Q: The number of edges in a graph with 10 vertices each of degree 5 is O 10 O 25 O 50

A:

Q: Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. How…

A: Given : Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and…

Q: Construct a connected simple graph, that has no circuit, with vertices M, N,0, P, Q, R, S, T, U such…

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Q: . Which complete bipartite graphs Km,n, where m and n positive integers, are trees? are

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.