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What is the worst-case running-time of the isGraphConnected function below which tests whether a graph G with n vertices and m edges is connected.

What is the worst-case running-time of the isGraphConnected function below which tests whether a graph G with n vertices and m edges is connected.

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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What is the worst-case running-time of the isGraphConnected function below which tests whether a graph G with n vertices and m edges is connected. Algorithm isGraphConnected(G) Input: graph G Output: true if G is connected and false otherwise v <- a vertex in G DFS(G) starting at v foreach u in G.vertices) do if u was not visited by DFS then return false return true a. O(mn) O b. O(n 2+mn) O c. O(n 2) O d. O(n 3) e. O(n+m)
Transcribed Image Text:What is the worst-case running-time of the isGraphConnected function below which tests whether a graph G with n vertices and m edges is connected. Algorithm isGraphConnected(G) Input: graph G Output: true if G is connected and false otherwise v <- a vertex in G DFS(G) starting at v foreach u in G.vertices) do if u was not visited by DFS then return false return true a. O(mn) O b. O(n 2+mn) O c. O(n 2) O d. O(n 3) e. O(n+m)
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