Answered: hat is obtain from G − ε by merging 2…

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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*Discrete Math

In the graph above, let ε = {2, 3}, Let G−ε be the graph that is obtained from G by deleting the edge {2,3}. Let G∗ be the graph that is obtain from G − ε by merging 2 and 3 into a single vertex w. (As in the notes, v is adjacent to w in the new if and only if either {2,v} or {3,v is an edge of G.)

(a) Draw G − ε and calculate its chromatic polynomial.

(b) Give an example of a vertex coloring that is proper for G − ε, but

not for G.

but not proper for G − ε.

(d) Draw G∗ and calculate its chromatic polynomial.

(e) Verify that, for this example,
PG(k) = PG−ε(k) − PG∗ (k).

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