K, is the complete graph with nvertices. For what values of n does it has ) an Euler cireuit? (i) Hamiltonian eireuit? (a) n21 and nis an odd number, n23 (6) n22 and nis an odd number, n22 (c) n23 and nis an odd number; n22 (d) n23 and nis an odd number; n23

Q: 130383&cmid=85723&page%3D1#question-175468-7 陶☆ ma19c022 Neeraj singh Let G be a simple connected…

A: Given: G is simple connected planar graph without having an induced graph k3

Q: Let G be a simple plane graph with fewer than 12 faces, in which each vertex has degree at least 3.…

A: Step 1: Consider the provided question, (17) (i)

Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: Providing the answer for first three parts if you want the answer of other parts please provide us…

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

A:

Q: (2) (a) Is the triangulated space ABD, BCD,CED, ABF, BCF, AEF, ADF, AED on a surface? (b) Let y be a…

A: 2 a) The triangulation of hexagon ABCDEF is given by Hence ABD,BCD,CED,ABF,BCF,AEF,ADF,AED forms a…

Q: Let G be a connected cubic graph of order n > 4 having clique number 3. Determine x(G).

A: Given- G be a connected cubic graph of order n>4 having clique number 3. To Find- The value of χG…

Q: (i) Use Euler's formula to prove that, if G is a connected planar graph of girth 5 with n vertices…

A: According to the given information, for part (i) it is required to prove that if G is connected…

Q: Draw a simple graph (or argue why one cannot exist) that (a) has 6 vertices, 12 edges, and is…

A: (a)Such a graph is not possible as we can seeK3 has 3 vertices 3 edgesK2 has 2 vertices and 1 edgeK4…

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: Use Ore's theorem to prove that any n-vertex graph G for which |E(G)|> (",') +2 is Hamiltonian.

A: answer is in next step

Q: Problem 4: The parts (a) and (b) of this problem are independent of each other. G1 G2 6 (a) Prove…

A: we are given two graphs G1 and G2

Q: a) Show that if G is a simple graph with n vertices (where n is a positive integer) and each vertex…

A: Part(a): G is a simple graph with n vertices and degree of each vertex in G is at least n-12. We…

Q: Determine the largest positive integer k such that χ(H) = χ(G) = k, where H is obtained from a…

A:

Q: Let Gbe a simple graph with at least 11l vertices, and let G be its complement. (i) Prove that Gand…

A: Given: G is a simple graph with at least 11 vertices and Ḡ be its complement.

Q: Coxeter

A:

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: Prove that every graph G on {1,... n} which is acyclic and has n 2 edges has exactly 2 connected…

A: Given: To prove the given statement as follows:

Q: USG hG FOlloing graph of P'(X) tO UGS GriDG thG benavior of fCX). Srate where P() ld inGrcasiNg…

A:

Q: y? xy = 1 has by checking for each of x2 a. Without using the graph, explain what symmetries them…

A: Given: x29-y264-xy=1 To check: The given function is symmetric about x-axis, y-axis or origin.

Q: 3. (MS) Select all that are true. a. Every graph has a vertex cover of size 0. b. Every graph has a…

A: Vertex cover V' of an undirected graph G=V,E is defined as a subset of V such that  if uv∈E implies,…

Q: 16 10 14 23 21 12 19 20 17 15 13 (c) graph. If no, try to use Euler's Formula and some estimate to…

A: To check if the given graph is planar. If yes, to find the number of regions of the planar graph. If…

Q: Let G be a bipartite graph with bipartite blocks with |A|| A = v1, v2, ..., Vm and B = u1, U2, ...,…

A:

Q: 2. Prove the following and make a sketch. a) Prove that every Eulerian graph of odd order has three…

A: 1. Since G is connected, every vertex has positive degree. Since G has an Eulerian cycle, every…

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: -) Reduce the given q vadratic equotion to canonical equation of a the graph. x2+4²+z²+4xy-4x2…

A: Given equation x2 + y2 + z2 + 4xy - 4xz + 4yz - 2x + y -3z = 0

Q: Let D be a domain and l be a closed line segment lying in D. In ele- mentary topology it is shown…

A:

Q: c) Prove that if a plane graph G has n vertices, e edges, f faces and k components then n- e+f =k+1.

A: We can prove Euler's formula (n-e+ f = k+1) works generally for anyconnected simple planar graph.so,

Q: (a) Compute degree centrality of all vertices. (b) Compute betweenness centrality of all vertices.…

A: Degree centrality of a vertex is defined as number of edges linked to that vertex or number of links…

Q: Suppose a graph G has 22 vertices. What is the minimum number of EDGES that G must contain if Diracs…

A: Dirac's theorem Let G = (V,E) be a graph with n vertices in which each vertex has degree at least…

Q: Find the total length of the graph of the astroid x2/3 y2/3 = 4.

A:

Q: List all the odd vertices of the graph. b) According to Euler’s Theorem, does the graph have an…

A: (a) The odd vertices are the vertices that have odd degrees, that is, having odd number of edges…

Q: Determine whether every graph in Kmn Wwhere n = m and n > 1 has a Hamiltonian cycle or path. Prove…

A:

Q: A complete m-ary tree of height h has. _number of vertices mh+1+1 A m+1 mh+1-1 (B h-1 mh -1 т-1…

A: If every leaf of a full m-ary tree is at the same level, then it is called a complete m-ary tree .

Q: 8. Find the perimeter of the sideways kissing-fish shaped region enclosed between the graphs of y…

A: arc length  in 2d L=∫abds  where ds = dx2+(dy)2 for the function of the form y =f(x)

Q: 3) What is the adjacency matrix Ac for the following graph G based on the order of the vertices a,…

A: Note: Since you have asked multiple independent questions, we are only allowed to answer one. Thank…

Q: Let H be a connected planar graph with at least 3 vertices. Prove that f is greater than or equal to…

A:

Q: a. Show that K2,3 is a planar graph by drawing it without crossing edges. b. Identify the number of…

A: The solution is given as follows

Q: Let Q be the pyramid with vertices Co,pp),(3,0,0), (3,6,0), (0,6,0),'and (0,0,6), a) sketch Q. 6)…

A:

Q: 7. a) How many different paths of length 2 are there in the undirected graph G in Fig. 11.43? b) Let…

A: Path : A path in a graph is a finite or infinite sequence of edges which joins a sequence of…

Q: Suppose that G is a graph such that uvory subgraph H of G contains a vortex of degree at most k…

A:

Q: 7. a, By using the theorem of Havel and Hakimi decide whether there exists a simple graph with…

A: According to Havel and Hakimi algorithm  the non increasing  sequence of degrees of vertices…

Q: a. Show that K5,6 has a path containing all vertices in the graph. b. Explain why K5,6 is not…

A: Hamiltonian graph - A connected graph G is called Hamiltonian graph if there is a cycle which…

Q: Which of the following is the adjacency ma- trix of the given graph? 1 2 4 3 [1 2 2 1 2 0 1 2 11 1 0…

A:

Q: 3. Consider a formula Vr3y3zVuE(x,y) ^ E(x, z) ^ (u = x v ¬E(u, y) V ¬E(u, z)). Here, x, y, z, u E V…

A:

Q: Give an example of a graph on 8 vertices which is i) Hamiltonian but not Eulerian. ii) Eulerian but…

A: A connected graph G is Hamiltonian if there is a cycle in G which covers every vertex of G exactly…

Q: 7. Give an (i) a non-planar graph that is not homeomorphic to K5or K3,3 example of

A: To find: A graph which is non planar and not homomorphic to K5 or K3,3. If the edges of the graph…

Q: Select the graph ofr = 4- 4sin 0. 15 11a 6 8 - lert

A: Option d

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.