How many different simple graphs are there om the vertex set [n]?

Q: 1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: (a) Show that in a simple graph with n > 2 vertices, at least two vertices have the same degree.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 10. A policeman wants to patrol a neighbarhood, but anly wants to walk down the street once. Based…

A: This is a problem of Graph Theory.

Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: Simply keep in mind that vertex degree multiplied by number of vertices is two times number of…

Q: Show that every graph with n vertices and k edges, n> k has n – k components.

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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: Are these graphs isomorphic? Yes because they have the same number of vertices Yes because they have…

A: Two graphs G1 and G2 are isomorphic if there exists a matching between their vertices so that two…

Q: number

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Q: When n = 3, there are nonisomorphic simple graphs.

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Q: How many non-isomorphic simple graphspre there with 11 vertices, 18 edges, minimum degree 3, maximum…

A: Given, Number of vertices V = 11 Number of edges E = 18 Minimum degree = 3 Maximum degree = 6 Number…

Q: . How many nonisomorphic directed simpe graphs are there with 4 vertices?

A: According to the given information, it is required to find number of non-isomorphic directed simple…

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: (b) Give an example of a disconnected simple graph on n vertices in which every vertex has degree…

A: We need to give an example of a disconnected simple graph on n vertices in which every vertex has…

Q: How many edges are there in a graph with 10 vertices each of degree six

A: The sum of degrees of vertices is, 6×10=60. Handshaking theorem: Let G=V.E is an undirected graph…

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: 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: Let n be a positive integer. Show that every connected graph on n vertices has at least n – 1 -…

A: This is a problem of Graph Theory.

Q: a. How many edges are there in complete graph K4,7 b. How many edges are there in complete graph…

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Q: 1. Let G be a complete graph with n vertices. a. How many edges does G have? Explain why. b. What is…

A: Solution of given problem as follow:

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

A: In the given question we have find the number of the distict graph with n verex.it's answer is "The…

Q: The set of all finite connected simple graphs is countable. O true O false

A: Here the given statement is 'the set of all finite connected simple ghaph is countable'

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: A graph with 7 vertices and 10 edges is shown. Vertex a is connected to vertex b, to vertex d, and…

A: According to the given information, First it is required to draw the graph from the given…

Q: Draw every simple graph with five vertices and four edges (isolated vertices are allowed) p to…

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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: Suppose we add two edges in a tree T to form a graph G. How many cycles can be there in G.

A: When 1 edges are added to a tree,  a cycles are created When 2 edges are added to a tree, either 2…

Q: (a) G is a connected graph with 6 vertices and 5 articulation points.

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Q: Let G be a simple, connected graph on n vertices (n≥3) Suppose that G has at least one cycle as a…

A: Given, G is a simple connected graph on n vertices with n≥3. G has at least one cycle as a subgraph…

Q: Draw a graph with two loops around vertex e, with end vertices a and f, with multiple edges on…

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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: Let G be a graph with n vertices and m edges, and let v be a vertex of G of degree k and e be an…

A: Degree of a vertex is defined as that from a vertex how many distinct edges are connected. Number…

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

A: Detailed explanation mentioned below

Q: A graph is connected if and only if one vertex is neighbor to all other vertices O True O False

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Q: How many edges are there in a 3-regular graph with 8 vertices?

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Q: Does there exist a graph G with 28 edges and 12 vertices each of degree 3 or 4?

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Q: A. If a simple graph G on 30 vertices has at least 301 edges, then its chromatic number is at least…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: G is a graph on 6 vertices with exactly

A: (b) G is a graph on 6 vertices with exactly two biconnected components:

Q: Let {6, 4, 3, 1, 1, 1, 0} be a degree sequence of a simple graph G. How many edges are there in the…

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Q: Let G be a graph with exactly 10 vertices and 27 edges. Suppose that each vertex has degree 3, 5, or…

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Q: 4. Draw every simple graph with five vertices and four edges (isolated vertices are allowed) up to…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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: A graph is called d-regular if every vertex has a degree of d. Let k and n be odd numbers, and prove…

A: Here we have to know the basic concept or the basic theorem before answering the question  THEOREM :…

Q: Is it possible for two different (non-isomorphic) graphs to have the same number of vertices and the…

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Q: Show all possible connected sub graphs of the following graph. How many of them are there refer to…

A: Given: a graph

Q: How many possible graphs can be created on 5 distinct vertices?

A: Consider a graph of n vertices.The line connecting any two vertices of a graph is called as an edge…

Q: Let K, be a graph obtained from K, by deleting one edge. How many subgraphs of K, are isomorphic to…

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Q: How many edges are there in a 3-regular graph with 14 vertices?

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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…