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

Q: Of the attached graphs, which could be a graph of y=ax³+bx²+cx+d if a,b,c,d all are real numbers and…

A: The given equation is, where  a,b,c,d are all real numbers and a<0.Now we determine the general…

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: Of the De AJKL has vertices J(2, 3), K(4, 5), and L(6, 1). Graph and label the vertices of AJKL and…

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Q: 4. Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5, 6} and edge-set = = {(1, 2), (3,…

A: Graph theory. Draw the graph, maximum and minimum degree of the graph

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 simple connected 6-regualar graph with 50 vertices. Then G is (i) a planar graph (ii) a…

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Q: 1. Below is a drawing of a graph G = (VG, EG), and then the vertex set and edge set of a graph H…

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Q: Let G be a simple undirected graph. Prove that (a) if G is disconnected, then d(GC) ≤ 2; (b) if d(G)…

A: Given: G is a simple undirected graph.To prove: a) d(Gc)≤2 if G is disconnected.                 b)…

Q: (b) a)

A: (a) The new Eularian graph is shown in the figure given in step 2.

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: 2. Draw a picture of the graph G specified as follows: Vertex set = {V1, V2, V3, V4, V5} Edge set =…

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Q: Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5} and edge-set E = {(1, 2),(3, 2),(4,…

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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 with vertex set V and edge set E. If |V] = 7, what is the largest value that |E||…

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

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Q: Let G be a simple graph that satisfies the following three conditions: (1) the graph G has 12…

A: Since the minimum degree (G) is at least 1, we know that each vertex in the graph has to be…

Q: "If G is a 3-regular graph, then K(G)=k'(G)", where K(G) is the minimum size of a vertex set S s.t.…

A: Given:  is a -regular graph, which means every vertex in  has a degree of  (i.e., each vertex is…

Q: Draw a simple graph G with 7 vertices and δ(G) ≥ 3 that has no Eulerian cycle, but has an Eulerian…

A: In the given question we have to draw a graph G with 7 vertices and δ(G)≥3has no eulerian cycle but…

Q: What does it mean to be "∆Y equivalent"? So for example K6 is ∆Y equivalent to the Petersen Graph?

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Q: Let P₁ and P₂ be two paths of maximum length in a connected graph G. Prove that P₁ and P2 have a…

A: First, we need to understand the problem. We are given two paths P1 and P2 of maximum length in a…

Q: A graph X is called self-complementary if it isomorphic to its complement. For a self-complementary…

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Q: B2. a For the following graph: H 1- Determine whether the graph is bipartite or not. University of…

A: ANSWER :

Q: (3) If possible, define graphs with the following properties. If not, explain why. (a) A graph with…

A: (a) The graph is defined.(b) The graph is not defined.(c) The graph is defined.Explanation:Step 1:We…

Q: 8. Graph G has vertex set V (G) = {u1, U2, U3, U4, U5, U6} and edge set E(G) = {e1, e2, e3, e4, e5,…

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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: Draw the following signal 3-3e-t/3 Please upload picure of your graph.

A: Given: Signal y(t)=3-3e-t/3

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: Complete a path straight at vertex a that ends at vertex c.

A: A complete path is defined when all the vertices are passed through and none of the smaller paths…

Q: Q. Let G be a connected graph. What is the relationship between bond of G and minimum edge cut of…

A: A bond with one edge

Q: B\ Prove that " there is no simple graph on four vertices, three of whic have degree 3 and the…

A: To prove: There is no simple graph on four vertices, three of which have degree 3 and the remaining…

Q: 9.1 Explain whether a graph with each of the following characteristics exists. If so, give an…

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Q: Draw a Cayley graph for Z/7Z with generating set {2¯,5¯}.

A: