1
GATE CSE 2004
+2
-0.6
Let $${G_1} = \left( {V,\,{E_1}} \right)$$ and $${G_2} = \left( {V,\,{E_2}} \right)$$ be connected graphs on the same vertex set $$V$$ with more than two vertices. If $${G_1} \cap {G_2} = \left( {V,{E_1} \cap {E_2}} \right)$$ is not a connected graph, then the graph $${G_1} \cup {G_2} = \left( {V,{E_1} \cup {E_2}} \right)$$
A
cannot have a cut vertex
B
must have a cycle
C
must have a cut-edge (bridge)
D
has chromatic number strictly greater than those of $${G_1}$$ and$${G_2}$$
2
GATE CSE 2004
+2
-0.6
What is the number of vertices in an undirected connected graph with $$27$$ edges, $$6$$ vertices of degree $$2$$, $$\,\,$$ $$3$$ vertices of degree 4 and remaining of degree 3?
A
$$10$$
B
$$11$$
C
$$18$$
D
$$19$$
3
GATE CSE 2003
+2
-0.6
$$A$$ graph $$G$$ $$=$$ $$(V, E)$$ satisfies $$\left| E \right| \le \,3\left| V \right| - 6.$$ The min-degree of $$G$$ is defined as $$\mathop {\min }\limits_{v \in V} \left\{ {{{\mathop{\rm d}\nolimits} ^ \circ }egree\left( v \right)} \right\}$$. Therefore, min-degree of $$G$$ cannot be
A
$$3$$
B
$$4$$
C
$$5$$
D
$$6$$
4
GATE CSE 2003
+2
-0.6
How many perfect matchings are there in a complete graph of 6 vertices?
A
$$15$$
B
$$24$$
C
$$30$$
D
$$60$$
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