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.
ethernet
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.
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
ethernet cable, ethernet hub, crossover cable, router
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 cables are used to connect many items. Such as:Printer to computer,Ps3 to laptop,ps3 to router