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Generally that would be no, you cannot, without a router your printer needs to have at least a connection to a computer (most likely via USB). Also at some point there has to be some kind of connectivity between your phone and your printer. the most common way is the link between all devices in a common LAN. But you could use something like Google's Cloud Print service if you have your Epson printer connected to a computer with online access. You'll be using your phone's cellular (mobile data) to link to Google's online Cloud Print which then connects to your Epson through your computer.Hi
Can I print from my Android phone to an EPSON Expression Home XP-435 All-in-One Wireless Inkjet Printer
at home without a router or wifi network?