Q7. For Theorems below give an example tree T with 15 vertices. Theorem 1. If a tree T is a wounded spider of order p, then y(T) = p - A(T). Theorem 2. If G is a connected graph, then [ diam (G)+¹1 ≤ (G). 3

Q: 12. Consider the algebraic expression E = (X + 3Y)*(a – 2b) draw a tree according to the equation!

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Q: 3. Find the tree and tree cover of Petersen graph. ***** *****

A: The Petersen Graph

Q: Answer the following questions: a.Suppose that a connected bipartite planar simple graph has e…

A: "Hey ,since there are multiple questions posted, we will answer first question. If you want any…

Q: >("₂¹). Let G be a graph of order n and size m such that m> connected. Make a sketch. Show that G is

A: As per the question we are given a graph G with order n and size m and it is given that…

Q: Could you please answer a,b and c

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Q: consider ihe foriowing polýnomiai functions 2 f(x) =-2x"+8 .hx): 3x(x3ー4) 4 please graph BötH

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Q: 4. Prove the following theorem: If a graph has more than two vertices of odd degree, then it does…

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Q: could you please answer d and e.

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Q: Q5. Suppose G is a graph of order 8 and suppose there are 2 vertices of order 7, 2 vertices of order…

A: Let G be a graph of order 8, in which there are 2 vertices of order 7, 2 vertices of order 6, 2…

Q: Statement. Let G be a connected graph. G is bipartite if and only if x(G) = 2. (a) We will first…

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Q: 1a. Prove: every tree with n ≥ 2 vertices has at least 2 leaves. (3 pt) 1b. Let T be a tree. Prove:…

A: Question 1a:Let T be a tree with n-vertices, n≥2.  We have to  prove that the tree has at least 2…

Q: If T₁ and T₂ are spanning trees for a graph G, then T₁ and T₂ have the same size. • Present your…

A: Graph theory Discrete mathematics

Q: Consider the graphs K,, K3 and K,, in figure given below. Find and draw an Euler 3,3 (traversable)…

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Q: 3. Prove: The sum of valancies ofvertices of a graph I, is twice the number of edges.

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Q: 2. Let G and H be a graphs. Prove that if G = H, then H= G.

A: Given: It is given that let G and H be a graphs , the objective is to prove that if and then

Q: Need help with this question. Please explain each step and neatly type up. Thank you :)

A: Theorem Statement:For k≥2 , every tree T with k vertices can be found as a subgraph in any graph G…

Q: 3. A simple graph H is the square of a simple graph G if V (H) = V(G) and xy is an edge in H if and…

A: The simple graph H is the square of another simple graph G if V(H)=V(G). xy is an edge in H if and…

Q: (6) Let G be a graph such that for any u, v € V(G), there exists a unique (u, v)-path. Prove that G…

A: G is a graph such that for any u, v∈VG, there exists a unique u, v-path. To Prove: G is a tree.

Q: Ouestion 3 (a) Suppose that T is a tree with n vertices, two of which have degrees r and s,…

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Q: (a) Prove that if a connected planar graph has 13 vertices and 12 edges then it must be a tree. (b)…

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Q: Prove: For any graph r with six vertices ror r complementary contains C3

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Q: (a) Show that n is even. (b) Show that T has + 1 leaves. (c) Determine the number of distinct graphs…

A: As per the question, we are asked to analyze a specific type of tree, denoted as T, with the unique…

Q: How can I prove the following: Let G be a 2-connected graph. If e and f are parallel edges in G,…

A: To prove that G\e is 2-connected, we need to show that for any two vertices u and v in G\e, there…

Q: Construct a simple graph that is a forest with vertices B,C, D, E, F,G, H,I such that the degree of…

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

Q: Let G be a connected graph and e and edge of G. Prove that k(G) = k(G - e) + k(G/e). Here k(G)…

A: Given  G be a connected graph and e an edge of G  we have to prove that kG=kG-e+kG/e here k(G)…

Q: Suppose G is a simple connected graph such that G is unicyclic. Prove that |V (G)| = |E(G)|.…

A: A cyclic graph has minimum of 3 vertices which is connected in a cycle and a graph is unicyclic…

Q: 4a Let n > 4. What is the maximum possible number of edges in a graph with n vertices and n-2…

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Q: can you please provide explanations

A: 1. Assumption: Start with the assumption that (G1​) and (G2​)are isomorphic graphs. 2. Definition of…

Q: (Prunes) Prove that if G is a tree with a vertex of degree d, then it has at least d leaves.

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: tree

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Q: 231 13 -82 14 17 25 19 to Consider the graph given above. Use Kruskars algortnm to find the minimum…

A: The smallest spanning tree is

Q: Prove the following theorem: If the graph G is a tree then there is a unique path connecting any two…

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Q: Let G₁ and G₂ be two distinct trees with the same vertex-set V. Prove that d(G₁)=d(G₂) if (G₁-x) =…

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Q: For any connected graph G of order 55, if x is a vertex of G, then the number of components of G-x…

A: A connected graph is graph that is connected in the sense of a topological space, i.e., there is a…

Q: 2. Draw all non-isomorphic trees of order n, where 2 < n < 6.

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Q: Select all that are true. a) For any bipartite graph G = (LUR, E), if |L| = |R| then ElEL deg(l) =…

A: Given: The statements regarding the bipartite graph.We need to check which of the given statements…

Q: Let T = (V, E) be a tree with V > 3 and k > 2 teaves. Prove that we can add k – 1 edges to T to…

A: Let TV, E be a tree with V≥3 and k≥2 leaves. Show that k-1 edges can be added to the graph of T to…

Q: 7. Prove: "If T is a tree of order n and size m, then m = n – 1." Give a concrete example to…

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Q: Determine if the following statement is true or false. If it is true, then prove it. If it is false,…

A: As per the question, we are asked to determine the truth value of a given statement about the…

Q: 6. (In this problem, y denotes the domination umber of a graph.) Let G be a graph such that (G) > 3.…

A: Let G be a graph. Such that γ(G)≥3. Prove that diam(G)≤2.

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

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