If a simple graph G is having I1 vertices and 9 edges then its complement graph G will have O 11 vertices and 46 edges O None of these O 11 vertices and 55 edges O 46 vertices and 11 edges

Q: If a simple graph G is having 15 vertices and 5 edges then its complement graph G will have None of…

A: 15 vertices and 105 edges

Q: 3. Find all connected sub-graphs of the following graph containing all of the vertices of the…

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Q: Let G be a simple connected graph with exactly 8 vertices, one of them has degree 7, and the other 7…

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Q: Let H be a graph If H has at least one vertex of degree greater than zero then there are two of even…

A: Given a graph representing H. Statement: If H has at least one vertex of degree greater than zero…

Q: If a simple graph G is having 10 vertices and 10 edges then its complement graph G will have 10…

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Q: Consider the problem Q defined below. Prove whether or not problem Q is in NP An undirected graph…

A: Given an undirected graph G(V, E) and a positive integer k.

Q: Suppose m and n are integers that are not zero together. Show that there is not always a graph with…

A: For a graph we know that,        Sum of degree of vertices = 2 x Number of edges.     => Sum of…

Q: Consider a complete graph with 6 vertices labeled A, B, F. (a) If you can start at any vertex, how…

A: Step-1 Consider a graph with 6 vertices, For complete graph with n vertices there exist   n-1!2…

Q: Let G be a graph without loop. If G has 6 vertices and 20 edges then the minimum number of edges…

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Q: If a simple graph Gis having 12 vertices and 9 edges then its complement graph G will have O 12…

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Q: Let Vn be the set of connected graphs having n edges, vertex set [n], and exactly one cycle. Form a…

A: Given Let Vn be the set of connected graphs having n edges, vertex set [n], and exactly one cycle.…

Q: Find the number of connected components for each of the following graphs. (a) A graph with 8…

A: (a) Given a graph with 8 vertices and 6 edges is shown. Vertex a is connected to vertex b and to…

Q: An edge is called a bridge if the removal of the edge increases the number of connected components…

A: We draw a graph without loop, find number of bridges by removing edges.

Q: For a given graph G having n vertices and e edges which is connected and has no cycles, which of the…

A: In the question it is provided that a graph G with n vertices and e edges is connected and has no…

Q: If v is a leaf of a graph and u is the vertex adjacent to v, then ε(v) = ε(u) +1. State whether…

A: Solution:- Given:- v is a leaf of a graph and u is the vertex adjacent to v. Yes, this statement is…

Q: Let G be a simple graph with n vertices, which is regular of degree d. By considering the number of…

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Q: Let Gbe a simple graph with at least 11l vertices, and let G be its complement. (i) Prove that Gand…

A: Given: G is a simple graph with at least 11 vertices and Ḡ be its complement.

Q: 1.1 How many simple graphs are there of four vertices? Draw all of them.

A: As per our guidlines we are supposed to solve only one question that is the first problem. For the…

Q: 4. Recall that a cut-vertex of a graph G is a vertex of G whose removal makes the graph dis-…

A: Definition: A vertex whose deletion along with incident edges results in a graph with more…

Q: Prove: For any graph r with six vertices ror r complementary contains C3

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Q: Prove that any graph with at least two vertices must have two vertices of the same degree.

A: Let G be a graph with n vertices where n≥2 To prove: G must have two vertices of same degree  On the…

Q: Suppose a graph G is connected and haas 106 vertices none of which have degree 1. What is the fewest…

A: We know that The minimum number of edges for undirected connected graph is (n-1) edges. But in this…

Q: 3.7 The complete tripartite graph K, consists of three sets of vertices (of sizes r, s and 1), with…

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Q: 7. Give an example of a simple graph that satisfies the specified conditions or show that no such…

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Q: 11. Either draw a graph with the specified properties or explain why no such graph exists. (1) Graph…

A: As per our guidelines I am solving only 1st 2. For others kindly resubmit the question mentioning…

Q: If a graph G has n vertices, all of which but one have odd degree, how many vertices of odd degree…

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Q: The complete tripartite graph K,, consists of three sets of vertices (of sizes r, s and t), with an…

A: Given that The complete tripartite graph Kr,s,t The graph of K2,2,2 in the following graph Hence,…

Q: If a simple graph G is having 13 vertices and 14 edges then its complement graph G will have O 13…

A: We have to solve given problem:

Q: Which of the following statements about a connected graph is always TRUE?         A path of…

A: Solution: From the definition of the connected graph there should be path between any two pair of…

Q: From the graph G given below identify the number of vertices and edges 6. A, 8. 4 C. O Vertices 3…

A: We have given a graph and we have to find the number of edges and vertices.

Q: Suppose that G is a k-regular graph of n vertices, and m edges. The vertex connectivity of G is…

A: Sol

Q: Let G be a graph with 10 vertice and 5 components. If a vertex is removed from G, the number of…

A: Answer: 9 and 4

Q: 14) For each of (a)-(c) below, either draw a graph with the specified properties or else explain why…

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Q: Prove or disprove: There exists some n > 1 such that there is a simple graph on n vertices, where…

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Q: Which of the following is always true for a connected graph? Select one: O a. all vertices have even…

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Q: Consider an undirected, connected, simple graph with n vertices. What are the minimum and maximum…

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Q: If G is a simple graph with at least two vertices. prove that G must contain two or more vertices of…

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Q: 5. For any graph G with six vertices, then G or its complement Ġ contains a triangle.

A: The solution for the above question is as shown below.

Q: [1] Write down the vertex-connectivity K(G) and the edge-connectivity 2(G) for each of the following…

A: Vertex connectivity: The minimum number of vertices required to disconnect the graph G is called…

Q: 2. Show that the graphs formed by deleting one edge from Ks and K33 are planar.

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Q: If a simple graph G is having 13 vertices and 7 edges then its complement graph G will have O 13…

A: Formula: If a simple graph consists n vertices and m edges, then its complement graph will consist n…

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

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Q: If a simple graph G is having 14 vertices and 13 edges then its complement graph G will have O 14…

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Q: Consider a complete graph with 6 vertices labeled A, B, ... F. (a) If you can start at any vertex,…

A: Consider the given information.   (a)   First calculate the number of Hamiltonian circuit in 6…

Q: Prove that in any simple graph G with n vertices and m edges, 2m ≤ n^2 − n.

A: We need to prove that in any simple graph G with n vertices and m edges, 2m≤n2−n

Q: Two simple graphs are if there is a bijection from the vertices of the first graph to the vertices…

A: To fill the correct answer in the blank space.

Q: The complementary graph G' of a simple graph G hasthe same vertices as G. Two vertices are adjacent…

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Q: Let G be graph with 8 vertices and 10 edges. If every vertex of G has degree 2 or 3, then How many…

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Q: .Given the following degree of the vertices of an undirected graph H = {4,1,5,3,4,3}, we can…

A: Sum of the degrees is 4+1+5+3+4+3=20, which is even. So H is a graph. Therefore, option C is not…

Q: Let G be a simple undirected graph with 16 edges. If all vertices have degree at most four, which of…

A: Let G be a simple graph with n vertices and e edges. Use the following formula, to determine the…

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.