For integers m, n ≥ 2, let Gm, be the graph with vertex set Vm,n = {(i, j) : 1 ≤ i ≤ m, 1 ≤ j ≤n} and edge set Em,n {((i1, J1), (i2, J2)) € Vm,n × Vm,n : |11 — i2|+|j1 − Ĵ2| = 1}. - 1. Find E2,2, E23, E3,3, E4,3 4, 7, 12, 17 separated by commas.) (Write your answers in the given order 2. Find the number of pairs (m, n) such that 2 ≤ m, n ≤ 10 and Gm, has an Euler cycle. 1 3. Find the number of pairs (m, n) such that 2 ≤ m, n ≤ 10 and Gm, has a Hamiltonian cycle. 81
For integers m, n ≥ 2, let Gm, be the graph with vertex set Vm,n = {(i, j) : 1 ≤ i ≤ m, 1 ≤ j ≤n} and edge set Em,n {((i1, J1), (i2, J2)) € Vm,n × Vm,n : |11 — i2|+|j1 − Ĵ2| = 1}. - 1. Find E2,2, E23, E3,3, E4,3 4, 7, 12, 17 separated by commas.) (Write your answers in the given order 2. Find the number of pairs (m, n) such that 2 ≤ m, n ≤ 10 and Gm, has an Euler cycle. 1 3. Find the number of pairs (m, n) such that 2 ≤ m, n ≤ 10 and Gm, has a Hamiltonian cycle. 81
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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Transcribed Image Text:For integers m, n ≥ 2, let Gm, be the graph with vertex set Vm,n = {(i, j) : 1 ≤ i ≤ m, 1 ≤ j ≤n}
and edge set Em,n = {((¿1, J1), (i2, j2)) € Vm,n × Vm,n : |i1 − i2| + |İ1 − İ2| = 1}.
1. Find E2,2, E23, E3,3|, |E4,3 4, 7, 12, 17
separated by commas.)
(Write your answers in the given order
2. Find the number of pairs (m, n) such that 2 ≤ m, n ≤ 10 and Gm,n has an Euler cycle.
1
3. Find the number of pairs (m, n) such that 2 ≤ m, n ≤ 10 and Gm,n has a Hamiltonian cycle.
81
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