2. Consider the following multigraph H:a) For k = 2,3,4,5,6,7, find a cycle of length k in H.b) Find a circuit of length 6 in H that is not a cycle.c) Find a circuit of length 8 in H that does not contain t.d) Find a circuit of length 9 in H that contains t and v.

Definitions: Circuit: Traversing a graph such that not an edge is repeated but vertex can be…

Answered: 2. Consider the following multigraph H:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q7. Construct an undirected network diagram using the given set of nodes and arcs: Nodes (A, B, C, D, E} Arcs (AB)=1, (AC)=3, (BC)=5, (CD)=1, (DB)=3,(DE)=1, (CE)=6}
Euler's Formula F + V = E+1 applies to any two-dimensional network where F is the number of regions formed by V vertices linked by E edges (or paths). Verify Euler's Formula for the network to the right. Choose the correct answer below. ? O A. 1+4 = 4 + 1 5 = 5 В. 2+5 = 6+1 7 = 7 ? C. 1+5 = 5+ 1 6 = 6 ? O D. 2+4 = 5+1 6 = 6
Plz answer both the question in 20 minutes
1. Which of the following is NOT a circuit in the graph? B E F Figure 1 OA) CBEC OB) ABEA 0 c) BCDCB OD) None of the Above
1.) For the following graphs, determine if they can be drawn with an Euler circuit, and Euler path or neither. а.) c.) b.) d.)
Which of the following graphs G = ({1,2,3,4, 5}, {a,b, c, d, e, ƒ}) have an Euler circuit? %3D Select one: O A. e = {a+ {4, 5}, b → {1,3},cH {1,3}, d → {2,3}, e + {2,5}, f → {4, 5}} = {a + {1,2},b → {2,3}, c→ {1,2}, d+ {3,5},e → {2, 4}, f → {4,5}} O C. e= {a→ {1, 2}, b → {2,3}, c→ {1,2}, d→ {2, 3}, e H {3,4}, f → {1,5}} O D. e= {a+ {4,5}, b → {1,3},CH {1,3}, d→ {2, 3}, e → {2.3}, f → {4,5}} O B. O E. E = {a→ {1,2},b→ {1,2}, c→ {2,3}, d→ {3,4}, e → {4, 5}, f → {4,5}}
4. A bipartite graph G with a bipartition (X, Y) is defined as follows: X = {a, b, c, d} and Y = {u, v, w}, and E(G) = {aw, bu, bw, cu, du, du, dw}. Draw the graph G.
Suppose we assign every element of Z x Z (think coordinate plane) one of three colors: cyan, magenta, or yellow. Show that there must exist a rectangle, with sides parallel to the axes, whose vertices are all the same color.
Is it possible to have an Euler Circuit in the above diagram? Justify.Is it possible to have an Euler Circuit in the diagram below? If there is an Euler Circuit, what is the path?
3
An Euler circuit of the graph K1 is, K1 (z, y, x, W, z, S, W) (V, z, X, W, z, s) (V, Z, x, W, z, s, W) a d. Not possible
Prove that if there is a circuit in a graph that starts and ends at a vertex v and if w is another vertex in the circuit, then there is a circuit in the graph that starts and ends at w.

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2. Consider the following multigraph H: a) For k = 2,3,4,5,6,7, find a cycle of length k in H. b) Find a circuit of length 6 in H that is not a cycle. c) Find a circuit of length 8 in H that does not contain t. d) Find a circuit of length 9 in H that contains t and v.