What will be the sum of all numbers in the neighborhood matrix of graph G? For n∈N we define the set Z_n={1,2,…,n-1} and on this set we define the modular product as follows: for x,y,z∈Z_n ∶(x.y=z)⇔(x.y≡z mod n). In other words, we get the number (z) by calculating the product of the numbers x and y as a common product of two natural numbers, and from this product we then calculate the remainder after dividing by the number n. Examples for n = 5 and different values of x and y: in Z_5 ∶ 3.4=2 , 2.3=1 , 2,4=3 … We construct the graph G so that its vertices are elements of the set Z_101 and the two vertices corresponding to the elements x and y are joined by an edge just when the set Z_101 holds: x.y = 1 in the sense of the modular product defined above.
What will be the sum of all numbers in the neighborhood matrix of graph G? For n∈N we define the set Z_n={1,2,…,n-1} and on this set we define the modular product as follows: for x,y,z∈Z_n ∶(x.y=z)⇔(x.y≡z mod n). In other words, we get the number (z) by calculating the product of the numbers x and y as a common product of two natural numbers, and from this product we then calculate the remainder after dividing by the number n. Examples for n = 5 and different values of x and y: in Z_5 ∶ 3.4=2 , 2.3=1 , 2,4=3 … We construct the graph G so that its vertices are elements of the set Z_101 and the two vertices corresponding to the elements x and y are joined by an edge just when the set Z_101 holds: x.y = 1 in the sense of the modular product defined above.
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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- What will be the sum of all numbers in the neighborhood matrix of graph G?
For n∈N we define the set Z_n={1,2,…,n-1} and on this set we define the modular product as follows:
for x,y,z∈Z_n ∶(x.y=z)⇔(x.y≡z mod n).
In other words, we get the number (z) by calculating the product of the numbers x and y as a common product of two natural numbers, and from this product we then calculate the remainder after dividing by the number n. Examples for n = 5 and different values of x and y:
in Z_5 ∶ 3.4=2 , 2.3=1 , 2,4=3 …
We construct the graph G so that its vertices are elements of the set Z_101 and the two vertices corresponding to the elements x and y are joined by an edge just when the set Z_101 holds: x.y = 1 in the sense of the modular product defined above.
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