**Question:**- If a graph is planar and has \( n \) vertices, can it have two vertices of degree \( n-1 \)? Can it have three vertices of degree \( n-1 \)? Justify your answer. **Question:**If a planar graph has 11 vertices and four times as many edges as faces, how many faces does it have? Is there a planar graph with 13 vertices that has three times more edges than faces?**Explanation:**This question involves understanding the properties of planar graphs and using the Euler's formula for planar graphs, which is:\[ V - E + F = 2 \]where \( V \) represents the number of vertices, \( E \) represents the number of edges, and \( F \) represents the number of faces.For the first part:- Given: \( V = 11 \) and \( E = 4F \).For the second part:- Given: \( V = 13 \) and \( E = 3F \).

If a graph is planar and has n vertices, it cannot have two vertices of degree n-1. However, it can…

Answered: If a planar graph has 11 vertices and…

If a planar graph has 11 vertices and four times as many edges as faces, how many faces does it have? Is there a planar graph with 13 vertices that has three times more edges than faces?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).

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