a. Prove that the sum of the degrees is equal to twice the number of edges. b. Check whether it is a simple graph or not. Give reasons.

Q: Which of the following graphs has seven vertices and exactly one bridge? O A. O B.

A: In this question, concepts of Vertices and Bridges are used. Vertices and Bridges A graph is made up…

Q: Find whether the following graph is bipartite or not. Explain your answer by your own. b) vs VA

A: A graph is a bipartite graph if its vertex set can be partitioned into two sets such that no two…

Q: Consider the following graph, where each node is labelled with a letter, and each edge has a number…

A:

Q: In the graph to the right, which vertex(vertices) is(are) adjacent to vertex C? D. B. .... Choose…

A: Graph: A graph is defined as G = (V, E) Where V is a set of all vertices and E is a set of all edges…

Q: (a) Give the number of edges in the graph.

A: answer is in next step. please give a like !!

Q: use Kuratowski's theorem to determine whether the given graph is planar. 23. а h 24. a he P 25. a

A: Planar Graph: A graph that can be drawn in the plane without any edges that cross each other where…

Q: A square with two diagonals drawn is a complete graph. True False

A:

Q: Determine whether the following graph is bipartite or not. Justify your answer either by giving a…

A:

Q: Can the following graphs drawn in plane without edge crossings? a

A: Given: Graphs, To determine: Whether the given graphs can be drawn without crossing.

Q: Consider the following graph. (b) How many trails are there from a to c? (c) How many walks are…

A: Given graph is

Q: (i) Verify the Hand-Shaking Theorem for the graph Go. a

A:

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: 1) Determine whether the graph shown has directed or undirected edges, whether it has multiple…

A: Directed graph: A directed graph is a graph in which all the vertices are connected together, where…

Q: 18. How many edges has each of the path graph P158? A. 155 B. 156 C. 157 D. 158

A:

Q: 26. How many edges are there in a graph with 10 vertices each of degree six? (a) 10 (b) 20 (c) 30…

A: We need to determine the number of edges in a graph that has 10 vertices each of degrees 6. We will…

Q: What kind of symmetry do the graphs have, if any?

A:

Q: If a graph has 10 edges, then what is its size? Answer:

A: Graph Theory:- The order of a graph is its number of vertices |V|. The size of a graph is its number…

Q: If the sum of the degrees in a graph is 18, then the number of edges is _____   a. 7     b. 9…

A:

Q: The word rock can refer to a type of music or to somethingfrom a mountain. Construct a word graph…

A: To find- The word rock can refer to a type of music or to something from a mountain. Construct a…

Q: Which graph is Eulerian? А. D С. D. H. B.

A: To identify which graph is Eulerian.

Q: if (a,6) is a point onthe graph y=x squared-x what is a

A:

Q: Consider the graph below. A C H D.

A:

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

A:

Q: Draw the union of the two simple graphs assuming edges with the same endpoints are the same. а f b f…

A: To explain the correct answer is given below.

Q: Is a complete graph with five vertices also a bi-partite graph? Justify your answer with drawings.

A: The solution is given below

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: . What is the order and size of the join of two graphs?

A: Given: To explain the given statement is given as,

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

A: If a connected planar graph G has e edges, v vertices, and r regions, then v-e+r=2. Here,  v=18,…

Q: A simple graph is _____.

A:

Q: Why is the graph K, a complete bipartite graph? a y K1 BI U EE s° S,

A:

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: If a connected graph with 12 edges splits the plane into 4 regions, then how many vertices should…

A:

Q: This refers to the number of edges incident to a particular vertex. Answer:

A: Explanation of the answer is as follows

Q: What is the number of edges and the degree of each vertex in a complete graph of a) n=15? b) n=19?…

A: We have to  find degree of  each vertex and number of edges of complete graph.

Q: Is the graph planar or nonplanar? Prove your answer.

A:

Q: 10. Determine whether the given graphs are bipartite or not. а. b. b d

A: Graph theory, bipartite graph

Q: Which of the following graphs has four vertices and exactly one bridge? O A. O B. OC.

A: I have given an answer in step 2.

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: If the sum of the degrees of vertices of graph G is 36, how many edges does G have? a. 12 b. 24…

A: We will use the theorem that the sum of the degree of graph G is equal to twice of number of edges.

Q: 3. Use the link to answer the parts a, b, and c from the previous question? Share the resulting…

A: Here probabilities are from given applet after calculating z score

Q: In a complete graph, if number of edges are 10, then the graph is: K2 K5 Kg K10 A Moving to another…

A:

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: In Exercises 9 to 12, determine whether the two graphs are equivalent. 10. B с A E D C D B E

A:

Q: The sum of the degree of vertices of a graph is always an even number.

A:

Q: The number of edges in a complete bi-partite graph Km.n is equal to n2 whenever а. m>n O b. m< n. O…

A: Since we know that "The number of edges in a complete bi-partite graph Km,n is equal to mn ".

Q: What is the number of connected components for each of the following graphs? (a) b a d

A: A connected component of an undirected graph is a maximal set of nodes such that each pair of nodes…

Q: The independent value is never used in reading a graph. O True O False

A: True

Q: How many edges are in the graph with n nodes where every pair of nodes are joined by an edge? Prove…

A: Given To find the number of edges are in the graph with n nodes where every pair of nodes are joined…