For any connected graph G of order 54, if x is a vertex of G, then the number of components of G-x must be

Q: Let G = (V, E) be a planar graph such that |V |< 19. Show that if the length of the shortest cycle…

A: For a given graph G=V,E where V≤19 that shortest cycle in G is 5, then we need to prove that G has a…

Q: Determine whether the graphs G and H are isomorphic

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Q: Suppose that an edge e ::= {v1, v2 } is on a cycle in a graph G where v1, v2 are vertices of G. If e…

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Q: Based on K1, K2, and K3, which graphs are not simple graphs? b a b. к, у K2 Y K3 Y K, and K2 a b K2…

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Q: Prove that if G is a graph with no isolated vertices, then α'(G) +β'(G) = n(G)

A: Here α'(G) is largest size of matching in G. β'(G) is the smallest size of an edge cover. We have to…

Q: G – v3 G- v2 G – v4

A: A graph consist of Set of vertices and edges A subgraph W of a graph G consist of subset of edges…

Q: Show that the two graphs below are isomorphism graphs GL: G2 : A B P D R S

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Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

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Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

A: Two graphs G and H are said to be isomorphic, if there exist a bijection f between their vertices…

Q: Let G be a connected graph that has exactly 4 vertices of odd degree: V1, V2, V3 and V4. Show that…

A: Let G be a connected graph which has 4 vertices of odd degree. The objective is to show that there…

Q: Give an upper bound on the number e of edges of G in terms of n and g if G is a connected plane…

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Q: Prove that a simple 2-connected graph G with at least four vertices is 3-connected if and only if…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let G be a connected graph with n(G) ≥ 2. Show that G at least 2 vertices which are not cut-vertices…

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Q: Draw a graph G with vertex and edge set  , where the endpoints of e1 are v1 and v2, the endpoints of…

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Q: Determine the largest positive integer k such that χ(H) = χ(G) = k, where H is obtained from a…

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Q: Let G =(V,E) be a finite graph on n ≥ 3

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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: to draw a graph for y=2x+5, a person can draw a point at x of 0 and y of _____, a second point by…

A: Given:

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: Show that if a simple graph G ha

A: To prove that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

Q: If a simple graph G is having I1 vertices and 9 edges then its complement graph G will have O 11…

A: Given, number of edges in graph G, EG=9 Number of vertices in graph G, n=11 We know that,…

Q: A K- regular graph is a graph where every vertex has degree K

A: Consider the given information. A graph is hamiltonian if it visits every vertex exactly once except…

Q: Prove that every graph G on {1,... n} which is acyclic and has n 2 edges has exactly 2 connected…

A: Given: To prove the given statement as follows:

Q: Find the smallest 3-regular graph G such that K(G) = 1.

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Q: Let G = (V, E) be a k-connected graph, let æ E V, and let B C V\{x} such that |B| > k. Show that…

A: Fan: Let v∈V(G) and let A∈V(G)\{v}. A v,A-fan of size k is a collection of k paths P1,P2,...,Pk so…

Q: True/False: If the graphs G1 and G2 are isomorphic, and G, is connected, then G2 must be connected…

A: If G1 and G2 are isomorphic , and G1 is connected

Q: If J has at least one vertex of degree greater than zero then there are two of even degree as long…

A: This is a problem of Graph Theory.

Q: Do the following: 1. Find a graph with 12 edges having six vertices of degree three and the…

A: We need to find a graph with 12 edges, such that 6 vertices have degree three and remaining all the…

Q: Let G be a connected graph of order n = 4 and let k be an integer with 2 ≤ k ≤ n − 2. a)Prove that…

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Q: If all the vertices in a graph G have degrees less than or equal to k, then x(G) _ k + 1. Fill in…

A: We can find the upper bound of the chromatic number of the graph if the degree of the vertices is…

Q: For any connected graph G of order 55, if x is a vertex of G, then the number of components of G-x…

A: A connected graph is graph that is connected in the sense of a topological space, i.e., there is a…

Q: True or false: If a connected graph G can be decomposed into exactly k paths then exactly 2k…

A: To Prove: A connected graph can be decomposed into exactly k paths then exactly 2k vertices of G…

Q: 6. (In this problem, y denotes the domination umber of a graph.) Let G be a graph such that (G) > 3.…

A: Let G be a graph. Such that γ(G)≥3. Prove that diam(G)≤2.

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: Show that every simple graph on n vertices is isomorphic to a subgraph of Kn.

A: We need to prove that every simple graph on n vertices is isomorphic to a subgraph of Kn (complete…

Q: The given graph is strongly connected. b True or False True False

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Q: Let H be a connected planar graph with at least 3 vertices. Prove that f is greater than or equal to…

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Q: Let G be a connected graph of order n = 4 and let k be an integer with 2 ≤ k ≤ n − 2. Prove that if…

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Q: If the graph G contains K, as a subgraph, then x(G) > n.

A: The chromatic number of a graph G  with vertex set V(G) is the smallest number of colures required…

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

A: Consider G be a simple connected graph with exactly 8 vertices, one of them has degree 7, and…

Q: For the given graph G, which of the following statements is false? A B) (F a) G is a simple directed…

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Q: Give an example of a non-planar graph that is not contractible to K5or K3,3.

A: Solution :-

Q: Let G be a simple graph with 20 vertices. Suppose that G h ponents, and every pair of distinct…

A: Given: Simple graph G with 20 vertices. G has two-component with distinct vertices that satisfy…

Q: Prove that if G is a graph of order p and has size greater than ¹) then G is connected. 2

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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: What is a(G) if G is a complete graph on n vertices?

A: It is given that G is a complete graph on n vertices. Also provided are some basic definitions about…

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.