1
GATE CSE 2015 Set 2
+2
-0.6
In a connected graph, bridge is an edge whose removal disconnects a graph. Which one of the following statements is true?
A
A tree has no bridges
B
A bridge cannot be part of a simple cycle
C
Every edge of a clique with size $$\ge 3$$ is a bridge (A clique is any complete sub-graph of a graph )
D
A graph with bridges cannot have a cycle
2
GATE CSE 2015 Set 2
+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, $$1$$ $$mod$$ $$4.$$
3
GATE CSE 2014 Set 1
+2
-0.6
An ordered $$n$$-tuple $$\left( {{d_1},\,\,{d_2},\,....,{d_n}} \right)$$ with $${{d_1} \ge ,\,\,{d_2} \ge .... \ge {d_n}}$$ is called graphic if there exists a simple undirected graph with $$n$$ vertices having degrees $${d_1},{d_2},.....,{d_n}$$ respectively. Which of the following $$6$$- tuples is NOT graphic?
A
$$(1, 1, 1, 1, 1, 1)$$
B
$$(2, 2, 2, 2, 2, 2)$$
C
$$(3, 3, 3, 1, 0, 0)$$
D
$$(3, 2, 1, 1, 1, 0)$$
4
GATE CSE 2014 Set 1
Numerical
+2
-0
Consider an undirectional graph $$G$$ where self-loops are not allowed. The vertex set of $$G$$ is $$\left\{ {\left( {i,j} \right):\,1 \le i \le 12,\,1 \le j \le 12} \right\}.$$ There is an edge between $$(a,b)$$ and $$(c,d)$$ if $$\left| {a - c} \right| \le 1$$ and $$\left| {b - d} \right| \le 1$$. The number of edges in this graph is _____.