What type of network cable is used to connect the router and switch?

Router and Switch --> Straight Cable

Switch and Switch --> Crossover Cable

Router and Router --> Crossover Cable

Switch and PC ---> Straight Cable

Thumbs Rule :

Similar devices --> cross cable

Different devices ---> straight cable

Cat5 and Cat6 Straight on Different Devices Cross on same Type Devices

Router and Switch --> Cat5e or Cat6 Cross cable Straight through  cable 

Cat5e or Cat6 Cross cable (Straight through  cable for Old model routers) or Fiber SC Type Patch cable .

Straight through Cable is used to connect different devices 

To Connact a router and a switch use straight through cable

devices belongs to different OSI layer will require Straight cable while devices belongs to same OSI layer will require Cross cable 

yeah, we can use cabl from Router to switch is straight through and we can use PC to Switch is straight through and Router to Router is Cross over cables speed is depending upon our requirement

straight-through  PC to switch, Router to switch, PC to Hub

UTP Cable Crossover connection are used to connect two different devices, like routers and switches.