In a typical H-R diagram, stars are graphed by these two characteristics:

The Hertzsprung-Russell (H-R) diagram graphs stars based on their temperature and luminosity. This diagram is a fundamental tool in astronomy to understand the properties and life cycles of stars. It was developed independently by Ejnar Hertzsprung and Henry Norris Russell in the early 20th century.

On the H-R diagram, the horizontal axis represents the star’s surface temperature, which decreases from left to right. The hottest stars appear on the left side and the coolest stars on the right. The vertical axis shows luminosity, which is the total amount of energy a star emits per second. Stars with higher luminosity appear at the top, and those with lower luminosity at the bottom.

By plotting stars on this graph, astronomers can group them into different categories, such as main sequence stars, giants, and white dwarfs. The position of a star on the H-R diagram helps predict its age, size, and future evolution.

Here’s why the other options are incorrect:
- **Luminosity and distance**: While luminosity is graphed, distance is not part of the H-R diagram axes.
- **Distance and temperature**: Distance is not used for graphing stars on the H-R diagram.
- **Size and distance**: Neither size nor distance is used on the H-R diagram’s axes.

In summary, the H-R diagram is a powerful visual tool that uses **temperature and luminosity** to classify stars and understand their properties across the universe.