Question

how many number of regions defined by a connected planar with 6 nodes and 10 edges option a 4 option b 6 option c 8 option d 10​

Answer 1

$\textbf{Given:}$

$\textsf{For a connected planar graph, number of nodes = 6}$

$\textsf{and number of edges=10}$

$\textbf{To find:}$

$\textsf{Number of regions}$

$\textbf{Solution:}$

$\underline{\textbf{Euler's formula:}}$

$\boxed{\mathsf{For\;a\;connected\;planar\;graph,\;\;V-E+F=2}}$

$\textsf{Here, V-Number of nodes}$

$\textsf{E-Number of edges}$

$\textsf{F-Number of regions}$

$\textsf{By Euler's formula,}$

$\mathsf{V-E+F=2}$

$\mathsf{6-10+F=2}$

$\mathsf{-4+F=2}$

$\mathsf{F=2+4}$

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

$\textbf{Answer:}$

$\mathsf{Option\;(b)\;is\;correct}$