(Discrete Math-Graph Theory) Let G=(V,E₁∪E₂∪E₃) be a simple graph such that G₁=(V,E₁) is planar, G₂=(V,E₂) is a forest, and G₃=(V,E₃) is a matching. Prove G is 9-colourable, i.e. its chromatic number satisfies χ(G)≤9.

Q: Let G be a simple graph with 11 vertices, each of degree 5 or 6. Prove that G has at least 7…

A: Given - G be a simple graph with 11 vertices, each of degree 5 or 6 To Prove - G has at least 7…

Q: b. An undirected simple graph in a star topology with one central vertex v such that E = {(v, x)/x e…

A: Reflexivity:Symmetric:

Q: Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,…

A: Solution:

Q: 4. (a) Define f : R×R→R×R by f(x,y) = (2x – y, x – 2y). Prove that f is one-to-one. Describe f-1.…

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Q: If A = {xeR: 2≤ x ≤5}, B = {xeR: − 2 ≤ x ≤ 1}, C = {xeR: -1 < x ≤ 1}. a) Sketch the graph of Cx…

A: information provided. However, I can guide you through the process of sketching the graphs of the…

Q: U₁ 1₂ U₂ Multiple Choice U₂ 1₂ V5 VI V4 22 e given graphs are isomorphic, then identify the correct…

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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: Select the graph for which a) ƒ¹(x) > 0 and f11(x) > 0

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Q: Which of the following graphs are isomophic? N N P P OA N

A: Two graphs are isomorphic if and only if their complement graphs are isomorphic. Two graphs are…

Q: .-) oketen a graph of p(x) =-21x-11 + 4 2 12 6-5 -4 -3-21 1 2 3 456 2 4 0-3 5 6 7. Given f (x) x24,…

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Q: Which of the following is the graph of (x+3)² + (y+4)² =257 -10-74444 -10-0744 T a . - → 7 "

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Q: Which of the following graphs are isomophic? (Choose two) F E E G D D H J J I A В E E G D H J J To…

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Q: 3) Let f(x,y) = 9x² + y² Statch the graph of fl

A: Sketch the graph of f(x,y)=9x2+y2

Q: = Let G be a graph and e E E(G). Let H be the graph with V(H) = = V(G) and E(H) = E(G)\{e}. Then e…

A: The objective of the question is to determine whether each edge in a given graph is a bridge, and to…

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: B C B H A Which of the following subgraphs S, T, U and V are vertex-induced subgraphs of R? Graph R…

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Q: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: E Consider the graph I: Which of the graphs below is isomorphic to I'? OA Z X B Z OC U Z Indicate…

A: Which of the graph is isomorphic to and indicate the isomorphism by listing the vertices.

Q: Consider a connected graph G and let e = uv € E(G) such that G' = G-e is disconnected. Let G₁ and G₂…

A: Let's go through each part of the problem step by step:Notation:- G: Connected graph.- e=uv∈E(G): An…

Q: Let G be the graph shown in the diagram below. V1 V2 V3 VA V5 V6 07 Is there a cycle of G that…

A: The given graph G is shown in the following diagram.We know that a Cycle in a graph is a non-empty…

Q: b) Prove that G = K2,12 is planar by drawing G without any edge crossings. (c) Give an example of a…

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Q: Please help me with this questions. I dont understand what I did wrong

A: We have to find whether the given pair of graphs are isomorphic or not Isomorphic graphs must have…