Question

The No. of edges of
Graph K10 is?
​

Answer 1

​$\underline{\textbf{Given:}}$

$\mathsf{K_{10}}$

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

$\mathsf{Number\;of\; \;edges\;of\;K_{10}}$

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

$\underline{\textbf{Complete graph:}}$

$\textsf{A graph in which any two distinct vertices are adjacent}$

$\textsf{is called a complete graph}$

$\mathsf{A\;compelte\;graph\;with\;n\;vertices\;is\;denoted\;by\;K_n}$

$\mathsf{Number\;of\;edges\;in\;K_n=n_{C_2}}$

$\mathsf{Number\;of\;edges\;in\;K_{10}={10}_{C_2}}$

$\mathsf{=\dfrac{10{\times}9}{1{\times}2}}$

$\mathsf{=5{\times}9}$

$\mathsf{=45}$

$\therefore\textbf{Number of edges in}\;K_{10}\;\textbf{is 45}$