Graph algorithms question - please answer both parts and prove or disprove them. Problem 1Prove or disprove the following statements:(a) Let G = (V, E) be a directed graph. For any uv € E, if some run of Depth-First-Search(DFS) on G results in v.f> u.f, then uv must be on a cycle.=(b) Consider any run of DFS on a directed graph G (V, E). For any edge uv € E, if there is apath from v to u in G, then uv cannot be a cross edge.

Disproved.The statement is not always true. Consider the following directed graph:v0 ----> v1…

Problem 1 Prove or disprove the following statements: (a) Let G (V, E) be a directed graph. For any uv E E, if some run of Depth-First-Search (DFS) on G results in v.f>u.f, then uv must be on a cycle. = (b) Consider any run of DFS on a directed graph G = (V, E). For any edge uv E E, if there is a path from v to u in G, then uv cannot be a cross edge.

Problem 1 Prove or disprove the following statements: (a) Let G (V, E) be a directed graph. For any uv E E, if some run of Depth-First-Search (DFS) on G results in v.f>u.f, then uv must be on a cycle. = (b) Consider any run of DFS on a directed graph G = (V, E). For any edge uv E E, if there is a path from v to u in G, then uv cannot be a cross edge.

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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