Learn Russian: Выпускник, получив диплом, решил искать работу. - Having received the diploma, the graduate decided to look for a job.

Получив is a perfective verbal adverb meaning "having received." It is formed by taking the past tense stem of the perfective verb получить (which is получи-) and adding the suffix -в. It indicates an action that was completely finished before the main action (решил) happened.

Is it possible to use получивши instead of получив?

You might hear it, but -вши is considered old-fashioned or overly colloquial for verbs whose stem ends in a vowel. In modern standard Russian, verbs like получить take -в. The -вши or -ши endings are generally required only when the stem ends in a consonant or if the verb is reflexive (like улыбнувшись).

Why are commas placed around получив диплом?

The phrase получив диплом is a verbal adverb phrase. In Russian, these phrases are almost always isolated by commas to show they are a supplementary background action, regardless of where they appear in the sentence.

What is the golden rule for who is doing the action in получив?

A strict rule for Russian verbal adverbs is that they must share the exact same subject as the main verb. Because выпускник (the graduate) is the subject who decided (решил), grammar requires that he is also the one who received the diploma.