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 $${G_1} \cup {G_2} = \left( {V,{E_1} \cup {E_2}} \right)$$

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?

The number of different $$n \times n$$ symmetric matrices with each elements being either $$0$$ or $$1$$ is

Consider the following statements with respect to user-level threads and kernel-supported threads.
i) Context switch is faster with kernel- supported threads
ii) For user-level threads, a system call can block the entire process
iii) Kernel-supported threads can be scheduled independently
iv) Use-level threads are transparent to the kernel

Which of the above statements are true?