Let E be the set of edges in the directed graph below, and let V be the set of vertices. Define a function h: E → V as follows: for any edge e E E, let h(e) be the vertex that edge e points at. Explain why this function is not onto. Be specific. y

Q: The figure below shows a directed acyclic graph G: O (C, E) O (C, A) O (C, G) F O (C, D) B A E Which…

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Q: Let h(u, v) = In(n – u? + v) + VVVD-u, Where n=666. Find its domain and sketch the Graph.

A: Given -  To find - Find its domain and sketch the Graph.

Q: (3) Suppose that G is a bipartite graph such that G = G(A, B). Show that G contains an even cycle.…

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A: # As per the guidelines we are entitled to solve three subparts at a time please resubmit the other…

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Q: 1.) 3 + 높+ 1! 2! + 6 3!

A: The solution is given as

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Q: G = (Z÷, '7

A: This is a problem of Group Theory.

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: 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: Let G = (V, E) be a connected graph with a bridge e = uv. Prove that there exist two disjoint sets…

A: Let us prove above result

Q: A 1-i

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Q: Suppose that A is the set {a, ß, y, d, ε}. A.) Construct a relation r on A that is a partial…

A: A relation r is said to be partial order relation if it is  (i) Reflexive  (ii) Anti-symmetric (iii)…

Q: When the graph of directed distance is decreasing, is the graph of velocity above or below the…

A: when the graph of directed distance is decreasing, velocity is negative so the graph of velocity…

Q: Is the relation with the directed graphs shown below an equivalence relation? 4. 6.

A: Let  A be a nonempty set. A relation ~ on the set A is an equivalence relation provided that ~ is…

Q: 13. Let A be the set A = {a, b, c, d}. Consider the relation R on A given by R = {(a, a), (b, b),…

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Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

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Q: Let A = {3,4,5,6} and B = {1,2,3} and define a relation R: A → B as follows: For all (x, y) ∈ A × B,…

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Q: Prove that if  v0 and v1  are distinct vertices of a graph  G  = (V,E) and a path exists in G from…

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Q: Let G = (V,, E,) and H = (V2, E2) be the following graphs: w G = (Vi, E1) H = (V2, E2) %3D a) Draw…

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Q: 8. Define a relation R on the set J = {0, 1,3,4,5,6} as follows: For all x, y EJ, x Ry ⇒ 4x² + y².…

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Q: Prove that if  v0 and v1  are distinct vertices of a graph  G  = (V,E) and a path exists in G from…

A: Let v0 and v1 be distinct vertices of a graph G=V,E. Assume that there exists path in G from v0 to…

Q: Let G be a graph, and let X(G) denote the chromatic number of G. If G is any planar graph, then x(G)…

A: Given G be a graph and let X(G) denote the chromatic no. of G.

Q: simple path in G from v0 to v1

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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: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

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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: Determine whether or not the two graphs G and G' pictured below are isomorphic. If so, define an…

A: The two graphs are NOT isomorphic.

Q: Which of the following graphs are isomophic? L A M N I K 식물 I N L B H D

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Q: b. Find an expression for the sum of the first n terms of the series 5+8+11+.. Hence, find the value…

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Q: Consider the following three graphs. Select one: o a. they are not isomorphic to each other. O b.Y…

A: 1. A graph G is an ordered pair VG,EG consisting of a non-empty set VG of vertices and a set EG of…

Q: Consider the following graph: a Define e d b x Ry iff {x,y} is an edge in the graph. Tick all the…

A: The statement "R is transitive" is false. {c,d} and {d,b}are edges of the graph. So c R d and d R b.…

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…

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Q: Let G be a bipartite graph of order p. Then i(G) ≤ 2.

A: please find the attached image

Q: Let G be a graph, and let x(G) denote the chromatic number of G. If G is any planar graph, then x(G)…

A: Let G be a graph and χG denote the Chromatic number. Here , G is planar graph. A graph is said to be…

Q: Now consider the graph G given by the following drawing. U6 11 u2 Uz us 15 V6 V5 V4 V3 01 ປາ (e)…

A: Detailed explanation: To find a maximum matching in the given bipartite graph 𝐺G, we need to select…

Q: Which of the following graphs are isomophic? F F E G E G DA C D H D H C C F F E G E G OB D D H D H C…

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Q: Let G = (V, E) be a k-connected graph, let æ E V, and let B C V\{x} such that |B| > k. Show that…

A: Fan: Let v∈V(G) and let A∈V(G)\{v}. A v,A-fan of size k is a collection of k paths P1,P2,...,Pk so…