Show that if and only if DFS(Depth-first Search) finds no back edges, the graph being traversed is acyclic.

Q: © Show that it is not possible to create degree 3 and 2 vertices of degree &. graph with 7 verlices…

A: By handshaking lemma, we get that the sum of degrees of all the vertices in a graph is two times the…

Q: Use the Greedy Algorithm to find a Hamiltonian circuit starting at vertex D in the weighted graph…

A: The nearest neighbor algorithm (NNA) is a greedy algorithm.  Follow the steps below to obtain an…

Q: Use the Chain Rule to compute In(u² +uv). au

A:

Q: prove that the maximum girth of a generalized Coxeter graph is 12, no matter what its parameters are

A: Among the generalized Petersen graphs, having n prism G p,1 on the Durer graph G 6.2 the…

Q: 4. Show that the edge set of every regular bipartite graph is a union of edge-disjoint perfect…

A:

Q: A 1-i

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Q: The fourth left-endpoint in a partition of [0, 3] with Ax = 0.5 is

A:

Q: find the minimum Hamilton circuit from the table starting at G. 10 10 12

A: Given The given table is Nearest Neighbor Algorithm→ i) Pick a starting vertex. ii) select the…

Q: 4. Find the lungth of le chord amd'its distane from the ankr. A 2.

A:

Q: Prove on the number of vertices that every graph G with n edges has a bipartite subgraph with at…

A: We will first assume that  P(n) : every graph G with n edges has a bipartite subgraph with atleast…

Q: 2. Apply Euler's Theorems and Fleury's Algorithm to determine Euler path and Euler circuits in each…

A: Euler Theorem states that If G is connected graph then G has Euler Circuit if and only if degree for…

Q: How many minimum spanning trees (MSTS) are possible in the ff. graph?

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Q: Euler’s Criterionoes.

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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: 2. Apply Euler's Theorems and Fleury's Algorithm to determine Euler path and Euler circuits in each…

A: Given:

Q: Find the and the sroallart Valurs of the functron fx)%=Ie+t on The intosval 0< ILI %3D

A:

Q: A connected multigraph has an euler path if and only if it has Every vertex has even degree Every…

A: Given that  A connected multigraph has an Euler Path if and only if it has.

Q: 2) Apply the Midpoint circle algorithm on a circle of center (0, 10), and radius 10. Indicate all…

A:

Q: Show that any graph with two or more nodes and no self-loops contains two nodes that have equal…

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Q: Use Dirac's Theorem to verify that the graph is hamiltonian and then find a hamiltonian circuit.

A: First name the vertex in given graph

Q: Show that the average degree of a vertex in the triangulation is strictly less than 6.

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Q: find rank(AT) and nullity(A)

A: Rank of A = rank of A^T use this relation

Q: find the number of the isomorphism classes of graphs with 5 vertices and 6 edges which have (i)…

A: Given the a graphs with 5 vertices and 6 edges. We have to find the number of the isomorphism…

Q: Prove that that any Sume with TH Convex Polyhedron has two faces of edges number

A: Let F be the face with greatest number of edges ,suppose n. There will be exactly 'n' other polygons…

Q: Apply Euler’s Theorems and Fleury’s Algorithm to determine Euler path and Euler circuits in each…

A: (a) Consider the given graph. Specify verticals and their degrees (the degree of a vertex is the…

Q: Prove: MA | (eahinlugnollipo)-3:(algm 41. Given: dirw 2ols Isosceles AMNP Ow with vertex P Isosceles…

A: This, can be proved by congruence rule

Q: 3. Find the distance between the polnts on the graph.

A: We have given two points.  And we have to find the distance between given two points.  Fir this we…

Q: Consider the graph in the attached. Give the order that the vertices are visited using Depth-First…

A:

Q: A connected multigraph has an euler path if and only if it has Exactly two vertices of odd degree…

A: Every time a circuit passes through a vertex, it adds twice to its degree. Since it is a circuit, it…

Q: -d-

A: We draw the figure as follows:

Q: If countries in the Southeast region are consisting of archipelagos then other foreign countries…

A: Euler diagram is a general diagram giving meaningful information about things that are related to…

Q: Find the maximal area of a right triangle with hypotenuse of length 1

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Q: Draw all graphs on 5 nodes in which every node has degree at most 2.

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Q: An outerplanar graph is a graph that admits a planar embedding with all vertices on the boundary of…

A: Given that an outerplanar graph is a graph that admits a planar embedding with all vertices on the…

Q: Define the hypercube Qn as follows. The vertex set of Qn is the collection of all 01-strings of…

A: Given the hypercube Qn is defined as follows: The vertex set of Qn is the collection of all…

Q: Euler’s Criterion.

A:

Q: Draw a directed graph with as few edges as possible that is strongly-connected, has 8 vertices of…

A: Strongly connected directed 8 vertices one has in-degree 3 two have cut degree 3 rest have samller…

Q: The optimal path for the TSP for a

A: Given, the optimal path for the TSP for a graph represented by the matrix  C=(cij), is given by the…

Q: Construct a graph for it, Build the Adjacency matrix for graph Eind Euler path

A: Given:

Q: Queshon 6) Compute the arthogonal projection of 8 onto the Line L through -S] and the origin. -6 LS.

A: We have to find the orthogonal projection of v on the line through P and the origin.

Q: 2. Apply Euler's Theorems and Fleury's Algorithm to determine Euler path and Euler circuits in each…

A: Solution :-

Q: Find the shortest path from vertex ‘a’ to ‘z’ by Dijkstra’s algorithm for the weighted graph

A:

Q: Let G be a pseudograph with 6 vertices. If G is having 3 loops and no parallel or multiple edges,…

A: A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted.…

Q: Prove that if a graph on n vertices is connected, and has n-1 edges, it must be acyclic.

A: A graph G is said to be a connected graph, if there is a path between any two vertices in that…

Q: 39 Show that humber of connecad regular graph with ald edges and whose number of rertices is…

A: We solve this following by using pigeonhole principle

Q: (a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is ("").…

A: Since the second question is independent of the first question, as per the guidelines I am answering…

Q: (g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A?

A:

Q: If fel²() and gelices. prove that fgeles.

A: Given that f∈L2(u), g∈L2(u) By definition If  g∈L2(u)⇒||g||L2&lt;∞

Q: Apply Dijkstra's Algorithm to find the shortest path from a to z in the following graph.

A: Let,lv=length l &amp; the vertx v from which it comes0=circle the visted vertex∞=length of…

Q: Find mZ1 in circle O. mAB = 42x, and 6x2. %3D mCD = %3D

A: Clearly we can see that chord BD is bisected by the radius OC. Hence,  mBC = mCD  mBC  =  (6x2)°…