1
GATE CSE 2021 Set 1
Numerical
+2
-0.67
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______
2
GATE CSE 2020
Numerical
+2
-0.67
Graph G is obtained by adding vertex s to K3,4 and making s adjacent to every vertex of K3,4. The minimum number of colours required to edge-colour G is _____.
3
GATE CSE 2015 Set 1
+2
-0.6
Suppose L = { p, q, r, s, t } is a lattice represented by the following Hasse diagram: 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
$$\frac{1}{5} < p_r < 1$$
4
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 ___________.