Question

A complete graph with 4 vartices has K edges where k is

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{A complete graph has 4 vertices and k edges}$

$\underline{\textbf{To find:}}$

$\textsf{The value of k}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\textsf{Number edges of a complete graph having n vertices is}$

$\mathsf{^n{C_2}}$

$\textsf{Here,}$

$\textsf{No. of vertices =4}$

$\textsf{No. of edges =}\;\mathsf{^4{C_2}}$

$\implies\mathsf{k=\dfrac{4{\times}3}{1{\times}2}}$

$\implies\mathsf{k=2{\times}3}$

$\implies\boxed{\mathsf{k=6}}$