I registered and created a new domain on Office 365 to experience O365 E3 trial version then created an application in Dot Net to send emails using graph API, both to same and different (gmail etc.) domains.
On coding side I don't see any error being produced, however on mail box side immediately I receive an email saying:
Delivery has failed to these recipients or groups:
**@something.onmicrosoft.com
Your message wasn't delivered because the recipient's email provider rejected it.
I am able to send emails from mailbox, manually by visiting https://outlook.office.com/
I am Office 365 global admin.