Constructing a Digraph: {1,2,3,4,5}

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In summary, for the relations "being a square of" and "being divisible without remainder by" on the set {1, 2, 3, 4, 5}, the digraph would consist of the following vertices: 1, 2, 3, 4, 5, with edges connecting 1 to itself (1,1) and 2 to 4 (2,4). This represents the relation "being a square of". For the second relation, the digraph would have edges connecting 1 to all other vertices (1,2), (1,3), (1,4), (1,5), and 2 to all other vertices except 5 (2,3),
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bird34
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Homework Statement



Construct a digraph for the relations: (i) being a square of and (ii) being divisible without remainder by on the set {1, 2, 3, 4, 5}.

Homework Equations





The Attempt at a Solution



{<1,2>, <1,3>, <1,4>, <1,5>, <2,3>, <2,4>, <2,5>, <3,4>, <3,5>, <4,5>}

I am completely lost and do not even know where to begin. Help!
 
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  • #2
first get the relations defined by them. for example if I understand (i), (x,y) belongs to the
relation R if y is square of x (x and y in the given set), then we can define the relation R as

[tex]R=\{(1,1),(2,4)\} [/tex]

Now to construct the digraph (or directed graph), refer to this link.
http://www.cs.odu.edu/~toida/nerzic/level-a/digraph/definition.html

It shows how to do this...And do similarly for the second relation
 

1. What is a digraph?

A digraph, short for directed graph, is a type of data structure used to represent relationships between objects. It consists of a set of vertices, or nodes, and a set of directed edges connecting these nodes.

2. How do you construct a digraph?

To construct a digraph, you must first determine the set of vertices and edges that will make up your graph. Then, you can use a variety of methods such as adjacency matrices or adjacency lists to represent these relationships in a computer program.

3. What is the purpose of constructing a digraph?

The purpose of constructing a digraph is to visually represent and analyze relationships between objects. It is commonly used in fields such as computer science, mathematics, and social sciences to model complex systems and make predictions.

4. What are some real-world applications of digraphs?

Digraphs are used in a variety of real-world applications, including social network analysis, computer networking, transportation and traffic flow modeling, and recommendation engines. They are also commonly used in visualizing and analyzing complex data sets.

5. What are some common algorithms used with digraphs?

Some common algorithms used with digraphs include breadth-first search, depth-first search, Dijkstra's algorithm, and topological sorting. These algorithms are used to traverse the graph and find optimal paths or order the nodes in a specific way.

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