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

Q: How many distinct unlabeled simple graphs on five nodes with equal to or less than five edges? 0 12…

A: The given question is related with graph theory. Here we have to find the number of distinct…

Q: Construct a graph with vertices F, G, H, I, J, K, L that has an Euler path, the degree of L is 1 and…

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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: In fig,draw a complete graph so that it has the type of symmetry indicated.

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Q: 3. Show that the two drawings represent the same graph by labeling the vertices and edges of the…

A: Give figure is

Q: In fig,draw a complete graph so that it has the type of symmetry indicated.

A: Given:  To determine: The complete graph so that it has the type of symmetry indicated.

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: 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: If a graph has vertices of degrees 1, 5, 2, 3, and 3, how many edges does it have? Why?

A: We are given a graph that has vertices of degrees 1,5 ,2, 3,3 Now, by Handshaking lemma we have: Sum…

Q: Does there exists a graph with the following degrees; (a) 0, 2, 2, 2, 4, 4, 6; (b) 2, 2, 3, 3,…

A: Given: the given degrees are (a) 0,2,2,2,4,4,6; (b) 2,2,3,3,4,4,5 To check : Does there exists a…

Q: 4. For each description, either draw a graph with the specified properties or explain why no such…

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Q: Consider the following graphs, each with vertex set V = {1, 2, 3, 4, 5, 6}, G = (V, E1), where E…

A: Given that,  V = { 1,2,3,4,5,6 }G1 = ( V, E1 ), where E1 ={{1,2},{2,3},{2,6},{3,5},{4,5},{5,6}}G2=…

Q: construct a graph with vertices Q,R,S,T whose degrees are 3,2,2,1  what is the edge set?

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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: 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: Consider the following directed graph. a. Give the indegree of each vertex. b. Give the outdegree of…

A: The vertices are {a , b , c , d , e} (a) The indegree of the vertex is the number of edges coming to…

Q: 8. Please find the vertex and edge sets of the following graph Vy ez ez

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Q: 13. Determine whether the following graph is strongly connected. b.

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Q: 9. Verify that Euler's formula does not hold for a graph that is not connected: count the vertices,…

A: The given question is related with graph theory. We have to verify that Euler's formula does not…

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

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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: Consider the following graphs, each with vertex set V = {1, 2, 3, 4, 5, 6}, G1 = (V, E), where E =…

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Q: Does there exist a simple connected graph with vertices of the following degrees? If so, draw the…

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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: (a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3 and…

A: As per guidelines only (a) is to be solved. Here, we use properties of undirected graph.

Q: Which of the following statements about a connected graph is always TRUE?         A path of…

A: Solution: From the definition of the connected graph there should be path between any two pair of…

Q: A graph is symmetric with respect to the ________ if, whenever (x, y) is on the graph, (−x, y) is…

A: We have to fill in the blanks: A graph is symmetric with respect to the --- if, whenever x, y is on…

Q: 8. 1 Use Kuratowski's theorem to prove that the following graph is not planar.

A: To Prove- Use Kuratowski's Theorem to prove that the following graph is not planar.   Theorem used-…

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: 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 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: 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: Consider the graph G in Fig. 8-58. Find: (a) degree of each vertex (and verify Theorem 8.1); (b) all…

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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: 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: 20 8. Compute the crossing number for each of the following graphs.

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Q: What is the number of vertices in an undirected connected graph with 27 edges, E vertices of degree…

A: Introduction: The handshaking lemma asserts that when a group of individuals shake hands, an even…

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

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Q: 5. Determine whether the given pair of graphs is isomorphic. Us H G

A: We need to check if both have the same vertices and edges, their degree sequence, and the length of…

Q: The number of non-isomorphic simple graphs on 8 vertices, all of which have degree 2, is Select one:…

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Q: 5. What is the chromatic number of the below graphs:

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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: 10. If we have two different non-crossing drawings of the same connected graph, is it possible for…

A: 10. For a connected planar graph, the below equation is always followed.        v - e + f = 2 Here,…

Q: 4. Draw the following graphs:

A: Part b,Given,           fx=x2       if x<13-x  if x≥1

Q: Find the chromatic number of each of the following graphs. Give a careful argument to show that…

A: The given graph is:

Q: .Given the following degree of the vertices of an undirected graph H = {4,1,5,3,4,3}, we can…

A: Sum of the degrees is 4+1+5+3+4+3=20, which is even. So H is a graph. Therefore, option C is not…

Q: Construct a simple graph with vertices J,K,L,MJ,K,L,M whose degrees are 1, 0, 1, 0 respectively.…

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Q: A graph has vertices of degree 1,2,3,3, and 8. How many edges does it have?

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