An Ethernet switch can not fulfill the role of a router, unless it be a "layer 3 switch" also known as "multilayer switch", which has capabilities of both a switch and a router - and is more expensive than either (mainly because it is optimized for handling lots of traffic, quickly).
For a small network, you don't really need a router. Routers are used to divide larger networks into smaller subnets, for efficiency, security, and administration. Routers are also used to connect different branches of a company to headquarters, or to each other, via WAN technologies - the router's role, in this case, is to connect the Ethernet network of a company's branch, to a WAN technology.
To the switch the router is just another host, so it connects with a straight Cat 5 or Cat 6 cable.
The Ethernet port is used to connect a computer to a connectivity device such as a modem, router, switch,etc. Does so via an ethernet cable.
ethernet
A straight-through ethernet cable.
A straight cable is used to connect a PC to a hub, switch, or router.
Use a straight through cable, just as you would with a hub or switch.
Ethernet.
the router as ports commonly used for lan cannection is (Ethernet)
Ethernet
There are three types of cables used in paired connection of computers: crossover, straight-through, and rollover. Crossover cables are used to connect two devices directly, without a router or switch in between. Straight-through cables are typically used to connect a computer to a router or switch, while rollover cables are typically used to connect a modem to a router or switch.
ethernet cable, ethernet hub, crossover cable, router
crossover cables must be used between 2 devices from the same level like (pc & pc - Pc & router - router & router) but strait through cable used between 2 different levels like (pc & switch - router & switch )