. Consider the tree drawn below. a. Suppose we designate vertex e as the root. List the children, parents and siblings of each vertex. Does any vertex other than e have grandchildren? b. Suppose e is not chosen as the root. Does our choice of root vertex change the number of children e has? The number of grandchildren? How many are there of each? c. In fact, pick any vertex in the tree and suppose it is not the root. Explain why the number of children of that vertex does not depend on which other vertex is the root.

Q: b) Anwer these below mentioned questions about the given rooted tree. i m n i. Which vertex is the…

A:

Q: In a tree with 32 vertices, what is the sum of degrees?

A: Vertex is where two or more edges meet . The degree of a vertex is the number of edges originating…

Q: Which of these graphs are trees? b) d)

A: A tree is a connected graph which has no cycles in it. Equivalently, A connected  graph of n…

Q: Find the independence number, clique number, chromatic number, as well as optimal coloring for the…

A: Solution

Q: Determine whether the following graph is complete or not. If it is complete, determine the number of…

A: We now check whether the given graph is complete or not. If the graph is complete then we will find…

Q: Answer the following questions: a) List the descendant's vertices of vertex e? b) List the…

A: Hi, Thank you for the question. Since you have posted a question with multiple sub parts as per the…

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

A:

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: A graph with 8 vertices has degrees 1, 1, 2, 3, 5, 7, 8, and 9. How many edges does it have?

A:

Q: For a complete graph, match the number of Hamilton circuits for a given vertices. n = 3 [ Choose ]…

A: For a complete graph, We have to match the number of Hamiltonian circuits or a given vertices. The…

Q: For a complete graph, match the number of Hamilton circuits for a given vertices. n = 3 n = 4 6 n =…

A: Hamilton Circuit : A circuit that must pass through each vertex of a graph once and only once. Being…

Q: A tree has 99 edges. How many vertices does it have? 99 198 100 O 200

A: We will solve this by using formula of edges and vertices

Q: Having read the definition of trees, which of the following graphs are trees? Why? Draw each graph…

A: Given: Graphs with vertices and edges: a G=V,E, V=a,b,c,d,e and E=a,b,a,e,b,c,c,d,d,eb G=V,E,…

Q: 5. Given the social network among six friends, answer the questions. Jomar James Judiel John Jade a.…

A: Given

Q: Consider the following graph: A B E D How many vertices are there? How many edges are there? What is…

A:

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

A:

Q: Determine whether the graph is a tree. If the graph is not a tree, give a reason why. C D Choose the…

A: We have given a graph and we have to check this graph is tree or not.

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

A:

Q: Draw the three nonisomorphic trees with five vertices and say how many distinct labelings each of…

A: To find the three non-isomorphic trees with fives vertices and to compute the number of distinct…

Q: What vertices are on each level in this graph, if we take s = 2?

A:

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: How many spanning trees do the following graphs have? (a) The wheel graph W(4) on five vertices. (b)…

A: Solution:-

Q: Given the tree below, find the following. e) Which vertex is the parent of h? f) Which vertices are…

A: 1. d is the parent of h 2.sibling of o is p 3.ancestors of m are b,g,e,f

Q: A. Find the number of vertices, the number of edges, and the degree of each vertex of the following…

A:

Q: B A D C

A:

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: 1. Which of these graphs are trees? а) b) (p f) 2. Which of these graphs are trees? а) b) c)

A: There are two questions given . But according to rules of Bartleby, only the first question can be…

Q: can be on a non-planar graph. 5. A_ a) complete graph b) subgraph c) line graph d) bar graph 6. If a…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 12. Answer these questions about the rooted tree illustrated.. (a) Which vertex is the root? (b)…

A: If the vertex of a tree is designated as the root, then the tree is called the rooted tree. The…

Q: 5. The number of edges in a regular graph of degree 46 and 8 vertices is a) 347 b) 230 c) 184 d) 18

A: Lets find number of edges.

Q: Consider the following graph: B E How many vertices are there? How many edges are there? What is the…

A:

Q: 16. How many edges has each of the complete graph Kso? A. 1235 B. 1245 C. 1225 D. 2450

A:

Q: 3. How many vertices and how many edges do each of the following graphs have? | a) K4 a. C. c) W.

A:

Q: 1.) Given that a tree has 12 edges. Find the number of vertices of the tree. Explain your answer…

A: A tree with n vertices has n-1 edges. So it has 13 vertices.

Q: For each graph, determine if it is a tree or not and give its redundancy. 1. a. What is the depth of…

A:

Q: 2. How many edges has each of the following graphs: (a) K10; (b) K5,7; (c) Ws; (d) the Petersen…

A: We need to find the number of edges in K10,K5,7,W8. (According to Bartleby only first three subparts…

Q: How many vertices will the following graphs have, if they contain: (a) 18 edges and all vertices of…

A: According to the rule I only do the first three

Q: is The number of edges in a complete bipartite graph K5 O 15 O 20 O 30 O 10

A:

Q: Create a graph with six vertices and exactly two bridges. Which of the following graphs has six…

A:

Q: The number of edges in a graph with 8 vertices each of degree 7 is O 7 O 56 28 O 14

A: We have to solve given problem:

Q: Let H be the graph below: (a) How many trees, with vertex set [7], have H as a subgraph? (b) How…

A: NOTE : As per Bartleby guidelines, incase of multiple subparts, only first three are answered.…

Q: In a connected planar graph drawn with no intersecting edges, if there are 3 vertices and 8 edges,…

A: We can use the Eulers formula for the planar graph to find the number of faces.

Q: Refer to the graph attached, and answer the following 1. How many vertices are there? 2. How many…

A: A graph is attached, and we need to find answer to the following questions. 1. How many vertices are…

Q: B C 4 D A 10 9. J 4 E 3 2 G F さ

A:

Q: The level of the vertex 't' of the tree 6. ke m

A:

Q: Answer T if the graph or tree exists as described and F if it does not. 1. Connected graph with 9…

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: 4. Þescribe each graph below. Explain how many vertices and how many edges it has, and if it is a…

A: Graph theory

Q: 6. Þescribe each graph below. Explain how many vertices and how many edges it has, and if it is a…

A: Graph theory

Q: 19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which…

A: please see the attachment