Let $$\delta $$ denote the minimum degree of a vertex in a graph. For all planar graphs on $$n$$ vertices with $$\delta \ge 3$$, which one of the following is TRUE?

If $$G$$ is a forest with $$n$$ vertices and $$k$$ connected components, how many edges does $$G$$ have?

An operating system uses $$shortest$$ $$remaining$$ $$time$$ $$first$$ scheduling algorithm for pre-emptive scheduling of processes. Consider the following set of processes with their arrival times and $$CPU$$ burst times (in milliseconds):

Process	Arrival Time	Burst Time
P1	0	12
P2	2	4
P3	3	6
P4	8	5

The average waiting time (in milliseconds) of the processes is ________.

A system uses $$3$$ page frames for storing process pages in main memory. It uses the Least Recently Used $$(LRU)$$ page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? $$$4,7,6,1,7,6,1,2,7,2$$$