State whether the following statement is true or false. Justify your answer with a short proof or a counter-example Every even graph is regular.

Q: Vhich of these graphs are trees? a) b) f)

A: A tree is an undirected graph in which any two vertices are connected by exactly one path and having…

Q: Is hypercube graph Q4 planar? If not can you provide any bounds on it crossing number?

A: No, hypercube graph Q4 is not a planner graph.

Q: Decide whether the following statement is true of false. Prove your answer: If two graphs have the…

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Q: Are the following graphs connected? If a graph is not connected, explain why it is not. II

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

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Q: This is a Graph Theory problem. Which complete graphs are planar. Explain why.

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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: 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: Please draw a graph that is a proper subgraph of the following graph (by "proper subgraph", I mean…

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Q: Draw any graph that is not simple.

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Q: Determine whether the graph is connected. Which vertices are odd? Which vertices are even? А

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Q: Define a pseudo graph?

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Q: Use the Handshaking Lemma to show that a graph G always has an even number of vertices with odd…

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Q: The following graphs are isomorphic Select one: True O False

A: The graph are given above in the question.

Q: Suppose a (simple) graph G = (V, E) is regular with odd vertex degree. Prove that the number of…

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Q: Determine if the following two graphs isomorphic? If so give the 1-1 correspondence between their…

A: We know two graphs are isomorphic if we can find a one-to-one correspondence between the vertices.…

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

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Q: 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: Verify the Handshaking theorem of the following graphs

A: To verify : The Handshaking theorem for the following graphs: (a) (b)

Q: what is K-connected of a graph ? And give an example

A: Definition: A graph is said to be K- connected graph or K edge connected graph if after removed less…

Q: 11. Are the following graphs isomorphic? Explain how you know. U2 V2 V5 V3 V4

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Q: В. С. D. А.

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Q: How can one prove a graph is connected?

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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: Are the ff. two graphs isomorphic? 1 0 0 1 1 1 1 O False O True

A: Two graphs are isomorphic if one graph can be obtained from the other by relabelling the vertices.…

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: Are the following graphs isomorphic? Justify..

A: We clearly see that the first graph, say G1 contains two 3-cycles [one the smaller inside and the…

Q: The given graph below is strongly connected b. Select one: True False

A: Strongly connected graph

Q: Give an example of obtaining the complete graph?

A: A graph is a complete graph if  each pair of graph vertices is connected by an edge. The complete…

Q: Which of the following graphs are bipartite? I

A: A graph is bipartite iff graph does not contains any odd cycle.

Q: Determine whether these two graphs are isomorphic. Explain why or why not. a b h d G

A: We see, in H, swxyzvuts is a 8-cycle. But, in G, maximum length cycle is 6-cycle. that is girth of G…

Q: 2. Determine if the following two graphs are isomorphic. а) b)

A: (a) let us suppose  graph 1 graph 2 we have to find if graph is isomorphic or not

Q: State whether the following statement is true or false. Justify your answer with a short proof or a…

A: Consider the general case, Let G be k-edge connected graph then we shall rove that G is k connected.…

Q: (c) A complete graph with two connected components.

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Q: B: Fined the dual graph for Jollowing graphs the

A: Given

Q: Are the following 2 graphs isomorphic? Discuss your answer with appropriate reasoning.

A: Given two graphs. From the first graph, d(u1)=3d(u2)=3d(u3)=2d(u4)=2d(u5)=3d(u6)=3

Q: Determine whether two graphs are isomorphic

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Q: Prove the following. 1. Prove that the number of odd vertices of a graph is even.

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Q: Graph x >-2.

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Q: Are the ff. two graphs isomorphic? Us 46 O False O True

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Q: Are the ff. two graphs isomorphic? 一 一 一 1. 1. 1. 1. -

A: To find Are the ff. Two graphs isomorphic.

Q: A D Graph 1 Graph 2

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Q: Draw all subgraphs of this graph

A: Given: There are 3 vertices, hence there will be 23=8 sub graphs Graph nodes: Nodes is defined as…

Q: а. B 1 2 3. E D F G 6 b. 3 5

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Q: . Determine if the following graphs are isomorphic or not? If yes, show how are they isomorphic. If…

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Q: Give an example of a non-planar graph that is not contractible to K5or K3,3.

A: Solution :-

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

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Q: The graph with edges AC and BD is a connected graph. True False

A: We have to find , the graph with edges AC and BD is a connected graph or not.

Q: Find the union of the given pair of simple graphs.

A: Concept Used:- Union of two simple graphs G1 =(V1 ,E1 ) and G2 =(V2 ,E2 )  is a simple graph with…

Q: This exercise deals with truncated graphs.a. What is a truncated graph?b. Give a legitimate motive…

A: a)A graph in which a part of vertical axis does not start at 0 but it start at any other data point…