1
GATE CSE 2025 Set 2
Numerical
+2
-0

Consider the following algorithm someAlgo that takes an undirected graph $G$ as input. someAlgo ( $G$ )

1. Let $v$ be any vertex in $G$. Run BFS on $G$ starting at $v$. Let $u$ be a vertex in $G$ at maximum distance from $v$ as given by the BFS.

2. Run BFS on $G$ again with $u$ as the starting vertex. Let $z$ be the vertex at maximum distance from $u$ as given by the BFS.

3. Output the distance between $u$ and $z$ in $G$.

The output of someAlgo( $T$ ) for the tree shown in the given figure is $\qquad$ . (Answer in integer)

GATE CSE 2025 Set 2 Data Structures - Graphs Question 1 English

Your input ____
2
GATE CSE 2025 Set 1
MCQ (Single Correct Answer)
+2
-0

Let $G(V, E)$ be an undirected and unweighted graph with 100 vertices. Let $d(u, v)$ denote the number of edges in a shortest path between vertices $u$ and $v$ in $V$. Let the maximum value of $d(u, v), u, v \in V$ such that $u \neq v$, be 30 . Let $T$ be any breadth-first-search tree of $G$. Which ONE of the given options is CORRECT for every such graph $G$ ?

A
The height of $T$ is exactly 15.
B
The height of $T$ is exactly 30.
C
The height of $T$ is at least 15 .
D
The height of $T$ is at least 30 .
3
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0

Let G be a directed graph and T a depth first search (DFS) spanning tree in G that is rooted at a vertex v. Suppose T is also a breadth first search (BFS) tree in G, rooted at v. Which of the following statements is/are TRUE for every such graph G and tree T?

A

There are no back-edges in G with respect to the tree T

B

There are no cross-edges in G with respect to the tree T

C

There are no forward-edges in G with respect to the tree T

D

The only edges in G are the edges in T

4
GATE CSE 2020
MCQ (Single Correct Answer)
+2
-0.67
Let G = (V, E) be a directed, weighted graph with weight function w: E $$ \to $$ R. For some function f: V $$ \to $$ R, for each edge (u, v) $$ \in $$ E, define w'(u, v) as w(u, v) + f(u) - f(v).

Which one of the options completes the following sentence so that it is TRUE?
“The shortest paths in G under w are shortest paths under w’ too, _______”.
A
for every f : V $$ \to $$ R
B
if and only if $$\forall u \in V$$, f(u) is positive
C
if and only if $$\forall u \in V$$, f(u) is negative
D
f and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G
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