Question

How many edges does a complete graph of 5 vertices have?​

Answer 1

Answer:

For 3 vertices the maximum number of edges is 3; for 4 it is 6; for 5 it is 10 and for 6 it is 15. For n,N=n(n−1)/2. There are two ways at least to prove this.

Answer 2

Answer:Total number of edges in a complete graph of 5 vertices is 10.

Step-by-step explanation:

Given:The number of vertices on graph $= 5$.

To find:We have to find the number of edges of graph having 5 vertices.

Explanation:

Step 1:It is given that the number of vertices on the graph is 5 which are connected so they will form a pentagon.

Step 2: As we know the total number of edges in a complete graph of n vertices is given by,

⇒Total number of edges in a complete graph of n vertices $= n$ × $\frac{(n - 1)}{2}$

Step 3:On substituting the value of $n = 5$ in the above equation we get,

⇒  Total number of edges in a complete graph of 5 vertices $= 5$ × $\frac{(5-1)}{2}$

⇒  Total number of edges in a complete graph of 5 vertices $= 5$ × $\frac{4}{2}$

⇒  Total number of edges in a complete graph of 5 vertices $= 5$ × $2$

∴   Total number of edges in a complete graph of 5 vertices is 10.

Concept: A graph consisting of vertices and line segments such that every line segment joins two vertices and every pair of vertices is connected by a line segment is called complete graph.

In the mathematical field of graph theory, a complete graph is a simple un-directed graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).

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