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(2) Let G be a directed graph on n vertices and maximum pos- sible number of directed edges; assume that n ≥ 2. (a) Present such a digraph when n = 3 assuming the vertices are 1, 2, and 3. (b) How many directed edges are in such a G, in general, when G has n vertices? Justify your answer. (c) Is G, as specified in the problem, reflexive? Justify briefly.

(2) Let G be a directed graph on n vertices and maximum pos- sible number of directed edges; assume that n ≥ 2. (a) Present such a digraph when n = 3 assuming the vertices are 1, 2, and 3. (b) How many directed edges are in such a G, in general, when G has n vertices? Justify your answer. (c) Is G, as specified in the problem, reflexive? Justify briefly.

Database System Concepts
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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A directed edge from a vertex to itself counts. Explain each answer.

(2) Let G be a directed graph on n vertices and maximum pos- sible number of directed edges; assume that n ≥ 2. (a) Present such a digraph when n = 3 assuming the vertices are 1, 2, and 3. (b) How many directed edges are in such a G, in general, when G has n vertices? Justify your answer. (c) Is G, as specified in the problem, reflexive? Justify briefly. (d) Is G, as specified in the problem, symmetric? Justify briefly. (e) Is G, as specified in the problem, transitive? Justify briefly. (f) Is G as specified in the problem, antisymmetric? Justify briefly.
Transcribed Image Text:(2) Let G be a directed graph on n vertices and maximum pos- sible number of directed edges; assume that n ≥ 2. (a) Present such a digraph when n = 3 assuming the vertices are 1, 2, and 3. (b) How many directed edges are in such a G, in general, when G has n vertices? Justify your answer. (c) Is G, as specified in the problem, reflexive? Justify briefly. (d) Is G, as specified in the problem, symmetric? Justify briefly. (e) Is G, as specified in the problem, transitive? Justify briefly. (f) Is G as specified in the problem, antisymmetric? Justify briefly.
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