What is the number of vertices in an undirected connected graph with 27 edges, E vertices of degree 2, 3 vertices of degree 4 and remaining of degree 3?

Q: If a graph has 4 vertices with degrees 1, 2, 2, 3 how many edges does the graph have. Show such a…

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

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Q: 2. Show that there is no simple graph with six vertices of which the degrees of five vertices are 5,…

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Q: 1. Create a connected graph having 8 vertices and 15 edges. 2. Label vertices with A,B,C,D,E, F,G…

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Q: The number of even degree vertices in a simple graph must be even. O true O false

A: To state true or false given statement.

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

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Q: A graph G has 15 edges, three vertices of degree 4, two of degree 1 and the remaining vertices have…

A: We are given with the number of edges and we know that the number of degrees is equal to twice of…

Q: 1. Draw a simple graph with six vertices such that each vertex has degree three. How about drawing…

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

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Q: How many vertices will a graphs have if it contains 16 edges and all vertices of degree 2

A: Let G be a graph having 16 edges and all vertices having degree 2

Q: Does a simple graph on eight vertices of degrees 1, 1, 2, 2, 3, 3, 4, 4 exist? Either draw such a…

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

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: Suppose an n-vertex bipartite graph G has exactly k connected components, each of which has two or…

A: Given: The value of n vertex includes the bipartite graph G that has exactly k connected components…

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: (4) Show that it is not possible to define a graph with 5 vertices of degree 3, and 2 vertices of…

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Q: 6. Suppose that every vertex of a tree has either degree 4 or degree 1. If there are 100 vertices of…

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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: Could there be a graph with four vertices of degree 1,2,5 and 4? Explain why no such graph exists or…

A: To verify whether a graph with 4 vertices of degree 1,2,5 and 4 exist or not.

Q: Construct a graph with vertices I, J, K, L, M, N that has an Euler circuit and the degree of L is 4.…

A: Given that, I, J, K, L, M, N that has an Euler circuit and the degree of L is 4. We have to find the…

Q: Construct a graph with vertex connectivity 3, edge connectivity 4 and minimum degree 5.

A: It feels like graph isomorphic problem or something related to it. However, I can't prove it. I…

Q: We say that two distinct edges in a graph are adjacent if there is a vertex incident to both (the…

A: Solution

Q: If a graph has 8 vertices with odd degree (valence), what is the smallest number of edges that would…

A: Solution is done in step 2

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) Is it possible to have a forest with 13 vertices and 10 edges?

A: As per bartleby guidelines i can answer only one question at one time, kindly post rest question…

Q: At the end of the party with n people, everybody knows everybody else. Draw the graph representing…

A: Here, number of people are n. So, the number of nodes in the graph will be n.

Q: If a planar graph has 18 vertices and 26 edges, how many regions are determined when you draw t…

A: We have to solve given problem:

Q: Construct a simple graph with vertices F, G, H, I,J that has an Euler circuit and the degree of F is…

A: A graph is said to be simple if it has no loops and parallel edges. Degree of a vertex of a graph is…

Q: 5. Draw a 3-regular graph which has 12 vertices and at least one bridge.

A: To find - Draw a 3-regular graph which has 12 vertices and at least one bridge.       Definition…

Q: Construct a graph with vertices L,M,N,O,P,Q that has an Euler circuit and the degree of P is 4. What…

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Q: Compute the cycle index for the number of non-equivalent graphs with 6 vertices. How many are there?

A: Given:-                 Compute the cycle index for the number of non-equivalent graphs with 6…

Q: In a graph, there are 17 edges, 3 vertices of degree 2, and all the other vertices have degree 4.…

A: We are authorized to answer one question at  a time, Since you have not mentioned which question you…

Q: Can a simple graph exist with 9 vertices all of degree 5?

A: Handshaking lemma: In any graph, sum of degree of all the vertices is twice the number of edges…

Q: A forest contains 39 vertices and 36 edges. How many connected components does the graph have?

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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: 1. Does there exist a disconnected graph of order 10 having 36 edges? Explain.

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

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: dges does a graph have if it has vertices of

A: Introduction: A graph is a structure consisting of a collection of objects, some of which are…

Q: If a graph has 12 vertices with odd degree (valence), what is the smallest number of edges that…

A: At least 6 edges would have to be needed. You would want to add an edgeto each vertex that has odd…

Q: 4. Is the graph below bipartite? If so, list the vertices in the one part and the vertices in the…

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Q: Draw an undirected graph with six vertices, each of degree 3, such that the graph is:(a)…

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Q: Is it possible for a graph with 6 vertices to have degrees 2, 2, 2, 3, 5, and 9? (Loops are…

A: We know that numbers of vertices of odd degree in any graph is always even. We use this fact in step…

Q: Is it possible to have a connected graph with six (6) vertices of degrees 1, 1, 2, 2, 2, and 3? If…

A: in a connected graph, the sum of degree of all the vertices is twice the number of edges. therefore…

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: A graph contains 45 vertices. If two vertices have the same degree, they are not connected by an…

A: The graph has 45 vetices and it has two vertices of same degreebut they arre not connected by an…

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: Construct a graph with vertices I, J, K, L, M, N that has an Euler path, the degree of K is 1 and…

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Q: Draw a graph with five vertices in which each vertex is of degree 3.

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