When a vertex Q is connected by an edge to a vertex K, what is the term for the relationship between Q and K? * and K are "isolated." Q and K are "insecure." O Q and K are "adjacent." O Q and K are "incident."

Q: 4. Consider the following graph. ez es a. How many paths are there from v to vy? b. How many trails…

A: Image is attached with detailed solution.

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

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Q: 41. Vertex e is OA) an incident vertex OB) insecure vertex OC) isolated vertex OD) adjacent vertex

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Q: Suppose a graph G has 15 vertices and 38 edges. Which of the following statements is true? O 1. G…

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Q: When K100 and C47 share exactly 20 vertices, all of which are consecutive in C47, how many edges…

A: Total number of edges in K100 = (100*99)/2          =  4950 Total number of edges in C47  = 47 If…

Q: Let d be the highest degree of any vertex in a tree T, and let l be the number of leaves of T. What…

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Q: How many cut vertices does the path Pn has for n ≥ 1?

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Q: How many vertices and edges has each of the Platonic graphs?

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Q: Show that if n > R(6,6) and we partition the edges of the complete to 4 pieces then one of the…

A: According to the given information, it is required to show that:

Q: Consider the following figure: a. Input the degree number for each vertex Vertex Degree Vertex A…

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Q: 17. Find a path from A to A that passes through each edge exactly one time. If none exists explain…

A: An Euler circuit is a circuit that uses every edge of a graph exactly once and its starting and the…

Q: Given the tree below, find the following  a) Which vertex is the root? b) Which vertices are…

A: Here we use basic defnitions of tree

Q: Determine whether the following statement is true or false. In the graph below, the path B, E, K, I,…

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Q: In exercises, a through d, give V, the set of vertices, and E, the set of edges for the graph G. d…

A: Since the question has 4 parts, we are supposed to answer only 2 parts. So solution is given for a…

Q: 3. Determine the edge connectivity and the vertex connectivity of the following graph. Explain.

A: The vertex connectivity is the minimum number of vertex required to remove from graph to make graph…

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: Assume you have a graph with vertex set V = {A, B, C, D, E} and edge set E = {CD, CB, DA, DB, EA,…

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Q: Construct a simple graph that is a tree with vertices P,Q,R,S,T PQ,R,S,T such that the degree of R R…

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Q: The number of vertices in K is

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Q: What is the degree of vertex  E ?     (b) List all the even vertices and all the odd vertices.…

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Q: Draw the acquaintanceship graph that represents thatTom and Patricia, Tom and Hope, Tom and Sandy,…

A: Acquaintanceship graph: It is a model used to represent the relationship among people. We use a…

Q: Which of the following vertices are adjacent. 7

A: If two vertices are connected by an edge, they are adjacent Check the given vertices 3 and 2 are…

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: 4. Edge FE is adjacent to which edges? 5. Does this graph have any bridges?

A: 2) 4. Recall: In a graph, two edges are said to be adjacent, if there is a common vertex between the…

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: How many vertices will the following graphs have if they contain: (a) 12 edges and all vertices of…

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Q: are both incident with vertex w and z. Based on the graph below, the edges ez es ez ea e10 eg e b.…

A: Graph theory

Q: The number of edges for a complete graph K6 is O 20 O 30 O 15 O 10

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Q: 40. When a vertex Q is connected by an edge to a vertex K, what i the relationship between Q and K?…

A: This is a problem of graph theory.

Q: How many edges and vertices are there in KA ? a) 6 Edges and 4 Vertices b) 6 Edges and 5 Vertices c)…

A: Draw a complete graph with 4 vertices, to find the number of edges in K4.  Hence, the complete…

Q: Is there a simple graph on 5 vertices such that all have distinct degree? 1.If so, draw one. If not,…

A: 1. Consider the given statement "Is there a simple graph on 5 vertices such that all have distinct…

Q: What are the edges incident on v2? (b) What are the vertices adjacent to v2 ? (c) What are the…

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Q: For which values of n does the graph Cn have an Euler circuit?

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Q: How many edges are in the Hasse diagram that represents the poset ( {1, 3, 4, 6, 8, 12, 16, 18), I…

A: Solution

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: (е) а C f е

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Q: If there are 10 vertices in a tree, there must be edges. O 10 O 9 O 11 O 8

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Q: Consider a bipartite graph on the set A = {1,2,3,4,5,6} and B = {7,8,9,10,11,12}, where there is an…

A: Given: A bipartite graph is defined on set A={1,2,3,4,5,6} and    B={7,8,9,10,11,12}. Here there is…

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: Which of the following is NOT a path starting at vertex A and ending at vertex E? E в D O A, F, B, E…

A: The given question is related to graph theory. The solution is explained below.

Q: for which values of m and n are km,n regular?

A: Given: A simple graph is called regular if every vertex of this graph has the same degree. A regular…

Q: it true that the graph below must have Hamilton circuits? If so, determine the number of such…

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Q: 4. Find the perimeter of rectangle MNOP with vertices M(-2, 5), N(-2, -4), O(3, –4), and P(3, 5). MN…

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Q: ve the problem. raph has 5 vertices: four vertices of degree 3 and a vertex of degree 2. How many…

A: Here we have to find the number of edges in given graph.

Q: In order to eulerize the graph below, give the fewest number of edges that need to be duplicated. a…

A: Label the vertices of the given graph. Next we use the process of eulerization of the graph by…

Q: For which values of n does the graph Wn have an Euler circui

A: In the given question we have to find the value of n for which the graph Wn have an Euler circuit.…

Q: Find a matching for the bipartite graphs below or explain using Hall's condition, if no matching…

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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…

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: For which values of m and n does the complete bipartite graph Km,n have an Euler circuit?

A: Definitions: A Path in a directed graph G is sequence of edges in G. A Simple path is a path that…