Hadith 857 - Bab 133 (Etiquette of offering Greetings)
Chapter 6 (The Book of Greetings)

Abu Hurairah (May Allah be pleased with him) reported: Messenger of Allah (Peace be upon him) said, 'A rider should greet a pedestrian; a pedestrian should greet one who is sitting; and a small group should greet a large group (of people).''

[Al-Bukhari and Muslim].

The narration in Al-Bukhari adds: Messenger of Allah (Peace be upon him) said, "The young should greet the elderly.''

Hadith 858 - Bab 133 (Etiquette of offering Greetings)
Chapter 6 (The Book of Greetings)

Abu Umamah Sudaiy bin `Ajlan Al-Bahili (May Allah be pleased with him) reported: The Messenger of Allah (Peace be upon him) said, "The person nearest to Allah is one who is the first to offer greeting."

[Abu Dawud].

The narration in At-Tirmidhi is: The Messenger of Allah (Peace be upon him) was asked: "O Messenger of Allah! When two persons meet, who should greet the other first?'' The Messenger of Allah (Peace be upon him) said, "The person nearest to Allah (i.e., one who is more obedient and therefore closer to Allah will say: As-Salam first."