Substitute : No as a substitute for a noun

Examples
1. A : Kore wa dare no hon desu ka.
"Whose book is this?"
B : Watashi no desu.
"It's mine."
2. A : Akai kaban wa dare no desu ka.
"Whose is the red bag?"
B : Ruin san no desu.
"It's Mr. Lwin's."
3. A : Aoi no wa.
"How about the blue one?"
B : Arisu san no desu.
"It's Alice san's."

In a modifier { noun, like noun + no + noun, -i adjective { noun, etc., a modified noun can be replaced by no, when the referent is obvious between the speaker and the hearer. And omit one no in case of noun { no { no. Take Ruin san no hon for example. When hon is replaced by no, you may expect Ruin san no no. However, the correct form is Ruin san no.
Examples
1. A : Kore wa anata no kutsu desu ka.
"Are these your shoes?"
B : Iie, watashi no ja arimasen. Ruin san no desu.
"No, they aren't mine. They are Mr. Lwin's."
2. A : Kono aoi no wa doo desu ka.
"How about this blue one?"
B : Ee, sore o kudasai.
"That's good. I'll it."