What is the worst-case running-time of the isGraphConnected function below which tests whether a graph Gwith n vertices and m edges is connected.Algorithm isGraphConnected(G)Input: graph GOutput: true if G is connected and false otherwisev <- a vertex in GDFS(G) starting at vforeach u in G.vertices) doif u was not visited by DFS thenreturn falsereturn truea. 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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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

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

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Chapter1: Introduction

Section: Chapter Questions

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Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.

Question

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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