Euler Circuits. In Exercises 1-3, a graph is shown and some sequences of vertices are specified. Determine which of these sequences show Euler circuits. If not, explain why not
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- 36 Consider a directed graph where V = {a, b, c, d) and E = {(a,b), (b.c), (c,d). (a.c), (d.b)}. How many 3-cycles are in G=(VE) ? 00 01 03 2arrow_forwardIn a school, n+100 students have access to three software packages A, B and C. n-1 did not use any software n-2 used only packages A n-3 used only packages B n-4 used only packages C n-5 used all three packages n-6 used both A and B. where n is your arid number i.e. 19-arid-234 take n=234 a) Draw a Venn diagram with all sets enumerated as for as possible. Label the two subsets which cannot be enumerated as x and y in any order. b) If twice as many students used package B as package A, write down a pair of simultaneous equations in x and у. c) Solve the equations to find x and y. d) How many students used package C?arrow_forwardDetermine whether the given graph has an Euler circuit or an Euler path. a OA OB OC OD (d P b g e (A) Euler circuit-no, Euler path-no (B) Euler circuit -no, Euler path-yes (C) Euler circuit-yes. Euler path -no (D) Euler circuit-yes, Euler path-yes.arrow_forward
- Which of the following statements about a connected graph is always TRUE? A path of edges exists between any two vertices of the graph. There is an even number of vertices on the graph. There is an even number of edges on the graph. Every pair of vertices is joined by a single edge.arrow_forward3) Determine whether the sequence of vertices is a path only, a circuit, or neither in the given graph. Circle the options listed in the part related to the given sequence. A B D E H a) BHFG b) BF G→C ⇒F→B c) GFH →B⇒F⇒C⇒G C PATH ONLY PATH ONLY PATH ONLY CIRCUIT CIRCUIT CIRCUIT NEITHER NEITHER NEITHERarrow_forwardThe figure below shows a directed graph G: 1 3 2 4 Which edge is not in G 3. а. (1, 3) b. (2, 3) с. (3, 4) d. (4, 3)arrow_forward
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- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL