**Problem 23:**If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have?To solve this, we can use Euler's formula for planar graphs: \[ V - E + F = 2 \]Where:- \( V \) is the number of vertices- \( E \) is the number of edges- \( F \) is the number of facesGiven:- \( V = 8 \)- \( E = 15 \)Substituting these values into the formula:\[ 8 - 15 + F = 2 \]\[ F = 2 + 15 - 8 \]\[ F = 9 \]Therefore, the graph has 9 faces.

Answer :- We know from the Euler formula that v+f =e+2

Answered: 23. If a planar drawing of a graph has…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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23. If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have?