Math Problem Statement
Tentukan diketahui sebuah graf berarah E dengan himpunan V={v1, v2, v3, v4, v5} dan himpunan arah E={(v1, v2) (v2, v3) (v3, v4) (v4, v1) (v5, v5) (v5, v1)}gambar lah diagram dari graf E
Solution
The problem asks you to draw a directed graph (or digraph) based on the given sets:
-
Vertices (V):
-
Edges (E):
Steps to draw the directed graph:
- Vertices: Place 5 vertices labeled .
- Edges: Connect the vertices with directed edges (arrows) based on the following pairs:
- : Draw an arrow from to .
- : Draw an arrow from to .
- : Draw an arrow from to .
- : Draw an arrow from to , forming a cycle with .
- : Draw a loop from to itself.
- : Draw an arrow from to .
This will result in a directed graph where:
- There is a cycle connecting ,
- has a self-loop and is connected to .
Would you like a detailed image of the graph or further clarification?
Here are 5 related questions to expand your understanding:
- What is the difference between directed and undirected graphs?
- How do you identify cycles in directed graphs?
- What are the in-degrees and out-degrees of each vertex in this graph?
- What are the practical applications of directed graphs?
- How do self-loops affect the structure of a graph?
Tip: In a directed graph, the direction of edges is crucial for understanding relationships between vertices, unlike in an undirected graph.
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Math Problem Analysis
Mathematical Concepts
Graph Theory
Directed Graphs
Vertices
Edges
Cycles
Formulas
-
Theorems
Graph Cycles
Self-loops in Directed Graphs
Suitable Grade Level
University Level
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