Quite easily. In LabVIEW the terms "graph" and "chart" are not synonymous.
A "chart" is like a paper stripchart recorder, to which you continously add data, and the old data gets scrolled off to the left. There's a built-in buffer that can be adjusted. Thus, you can use a chart to display the most recent 10 seconds, and use the buffer to view the previous data.
A "graph" displays a fixed amount of data. There are 2 types of graphs: waveform and XY. The waveform graph is intended to be used when the samples are evenly spaced. The XY graph is intended when they're not.
As before, take a look at the examples that ship with LabVIEW. The "Charts" example shows a variety of ways to create a chart. In your case the loop time would be 1 second. You can use the while loop as shown in the example, or a timed loop (Programming -> Structures -> Timed Structures).