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For n EN we define the set Zn = {1, 2,. .. , n - 1} and we define modular product on this set as follows: for x, y, z E Zn: (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 of 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 Zg : 3.4 = 2, 2.3 = 1, 2.4 = 3... Assignment: We construct the graph G so that its vertices are elements of the set Z101and two vertices corresponding to the elements x and y will be joined by an edge just when the set Z101 holds: x.y = 1 in terms of the modular product defined above. a) Is the graph G regular? b) Is graph G continuous? c) Is graph G a tree?

For n EN we define the set Zn = {1, 2,. .. , n - 1} and we define modular product on this set as follows: for x, y, z E Zn: (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 of 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 Zg : 3.4 = 2, 2.3 = 1, 2.4 = 3... Assignment: We construct the graph G so that its vertices are elements of the set Z101and two vertices corresponding to the elements x and y will be joined by an edge just when the set Z101 holds: x.y = 1 in terms of the modular product defined above. a) Is the graph G regular? b) Is graph G continuous? c) Is graph G a tree?

Advanced Engineering Mathematics
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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Hi, I received solution for my assignment and I have question for it. I thought that for this graph should be 2 loops for 1 and 100. Then it also shouldn’t be regular graph. I added assignment and also solution as image. Thanks.
For n EN we define the set Zn = {1, 2,... , n - 1} and we define modular product on this set as follows: for x, y, z E Zn: (x.y = z) (x.V = 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 of 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; : 3.4 = 2, 2.3 = 1, 2.4 = 3. .. Assignment: We construct the graph G so that its vertices are elements of the set Z101and two vertices corresponding to the elements x and y will be joined by an edge just when the set Z101 holds: x.y = 1 in terms of the modular product defined above. a) Is the graph G regular? b) Is graph G continuous? c) Is graph G a tree? d) What will be the sum of all numbers in the adjacency matrix of graph G? The answers to all these questions must be duly substantiated, resp. proven.
Transcribed Image Text:For n EN we define the set Zn = {1, 2,... , n - 1} and we define modular product on this set as follows: for x, y, z E Zn: (x.y = z) (x.V = 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 of 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; : 3.4 = 2, 2.3 = 1, 2.4 = 3. .. Assignment: We construct the graph G so that its vertices are elements of the set Z101and two vertices corresponding to the elements x and y will be joined by an edge just when the set Z101 holds: x.y = 1 in terms of the modular product defined above. a) Is the graph G regular? b) Is graph G continuous? c) Is graph G a tree? d) What will be the sum of all numbers in the adjacency matrix of graph G? The answers to all these questions must be duly substantiated, resp. proven.
Now, the neighbarhood matrix of G is a 100x 100 matrix, where each aw carrespond to a vertex of G, and entry means ith vertex is adjoint ij to th vertex , Hence, in uz case, each row of the matrix will have one 1 and resto's, Then sum of entries in each row mly Then, sum of all numbers in the matrix= 100x1 - 100,
Transcribed Image Text:Now, the neighbarhood matrix of G is a 100x 100 matrix, where each aw carrespond to a vertex of G, and entry means ith vertex is adjoint ij to th vertex , Hence, in uz case, each row of the matrix will have one 1 and resto's, Then sum of entries in each row mly Then, sum of all numbers in the matrix= 100x1 - 100,
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