1
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67

Let G be any connected, weighted, undirected graph.

I. G has a unique minimum spanning tree, if no two edges of G have the same weight.

II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique minimum-weight edge crossing the cut.

Which of the above two statements is/are TRUE?

A

I only

B

II only

C

Both I and II

D

Neither I nor II

2
GATE CSE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Suppose L = { p, q, r, s, t } is a lattice represented by the following Hasse diagram: GATE CSE 2015 Set 1 Discrete Mathematics - Graph Theory Question 28 English For any $$x, y ∈ L$$, not necessarily distinct, $$x ∨ y$$ and x ∧ y are join and meet of x, y, respectively. Let $$L^3 = \left\{\left(x, y, z\right): x, y, z ∈ L\right\}$$ be the set of all ordered triplets of the elements of L. Let pr be the probability that an element $$\left(x, y,z\right) ∈ L^3$$ chosen equiprobably satisfies $$x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z)$$. Then
A
pr = 0
B
pr = 1
C
$$0 < p_r ≤ \frac{1}{5}$$
D
$$\frac{1}{5} < p_r < 1$$
3
GATE CSE 2015 Set 1
Numerical
+2
-0
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is ___________.
Your input ____
4
GATE CSE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on $$n$$ vertices, $$n$$ is
A
A multiple of $$4$$
B
Even
C
Odd
D
Congruent to $$0$$ $$mod$$ $$4$$, or, $$1$$ $$mod$$ $$4.$$
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