Let n e N with n > 2 and let G, = (V, E) be the graph with vertex set V = {v1, v2, . . . , v2n} and edge set %3D E = {{vi, vi+1} : 1

Q: 8. (a) Can you draw a graph with at least two vertices for which all the vertices have different…

A: consider the graph  A has valence 1 Vertex B has valence 2 Vertex C has Valence 3 Vertex D has…

Q: 5. Let G = (V, E) be a finite, connected graph. Show that if no vertex of G has degree less than 2,…

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Q: The graph of s gen Evle a/G). yA (1, 1) y = 1 (1,1/2) x=-1

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Q: 4. Prove: "Show that the number of edges in a simple planar graph of order n is at most 3n – 6".…

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

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Q: How many nonisomoprhic connected planar graphs (V, E) are there with v = 6 and e = 10 assuming that…

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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: A simple graph is called regular if every vertex of the graph has the same degree. An n-regular…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: What will vertex C' be if this figure is translated 8 units to the right and 6 units down? ) (1,3) )…

A: Solution: we have  C = (-5,5)

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: Q₁. Find the vertex connectivity K(G), edge connectivity K'(G) and minimum degree 8(G) of the graph…

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Q: Give an upper bound on the number e of edges of G in terms of n and g if G is a connected plane…

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Q: does planar graph of order 4 has an example? How about nonplanar graph of order 4? Can you give…

A: Hints: Give an example of planar graph and also nonplanar graph of order 4.

Q: 7. Prove : Every graph with radius r and girth with 2r +l is regular

A: To Determine :-  Every graph with radius r and girth with 2r +1 is regular.

Q: Prove that a simple 2-connected graph G with at least four vertices is 3-connected if and only if…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let n € N with n > 2 and let G₁ = (V, E) be the graph with vertex set V = {₁, V2, ..., V2n} and edge…

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Q: The complete bipartite graph K_(n,m) has chromatic number two..* false O True

A: Remark: The chromatic number of a graph G is the smallest number of colors needed to color the…

Q: 9. Which edges could be re-used in order to find an optimal Eulerization of the following graph? (1)…

A: The objective is find which edges that could be re-used to find the optimal Eulerization of the…

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

A: Sketch the graph of f(x,y)=9x2+y2

Q: e say that a graph is k-regular if each of its vertices is the endpoint of exactly k edges. Consider…

A: A k-regular bipartite graph G=X⊔Y, E, where 1≤k≤n. A graph is said to be k-regular if each of its…

Q: (4) Show that it is not possible to define a graph with 5 vertices of degree 3, and 2 vertices of…

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Q: the anea af Hhe iangle withe the vertices Alogogo), B=(211) C= (2っ33) %3D

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Q: Which one of the following is not a trail from vertex x to vertex y for the graph G=(V,E), if…

A: In graph theory,Trail is a open walk where vertices may repeat but edges can't .

Q: 2) Graph a) y = x2 + 4x + 1 o b) y = x2 – 4x + 1

A: Let's find.

Q: How can I prove "A graph is k-colourable if and only if it is k-partite.”?

A: As per the question we have to prove that a graph is k-colourable if and only if it is k-partite. To…

Q: 1. Graph ysx+1 12 A solution is:

A:

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: 11. Given: V = {1,2,3,4,5) E = {(1,2), (1,3), (1,4), (1,5), (2,4), (2,5), (3,4)} a) Draw the graph G…

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Q: 5 (i)

A: Answer for  sub question a: Given graph is, G=V,E,V=a,b,c,d,e, E=∅ 1) Note: A vertex with no…

Q: 2.29. Is this graph planar (the edges cross each other in the middle but there is no vertex there)?

A: Planar graph: When a connected graph can be drawn without any edges crossing it is called planar.…

Q: Which of the following four graphs on five vertices is not isomorphic to any of the other three?…

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Q: Give a family of graphs of order p such that t(G) = 2.

A: The family of graphs of order p such that γtG=2 are given below.

Q: 7. Let G be an undirected graph with vertex and edge sets given below: V = {1, 2, 3, 4, 5, 6}, E=…

A: The given graph G is an undirected graph (the graph in which the edges do not have a direction). The…

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: 1) The vertices of AHEN are H(0, 4), E(6, 4), and N(4, -2). AH'E'N' is the image of AHEN after Dox.…

A: If we are dilating a point (x,y) about the origin by a scale factor (dilation factor) of k, then the…

Q: Prove that every simple graph G= (V, E) with |V] > 2 has at least two vertices of equal degree. %3D…

A: We have a simple graph, with V≥2, that is, the number of vertices is greater than or equal to 2.…