Slitherlink
Slitherlink (also known as Fences, Takegaki, Loop the Loop, Loopy, Ouroboros, Suriza and Dotty Dilemma) is a type of path-drawing logic puzzle designed and published by Nikoli. Slitherlink puzzles are traditionally solved on a rectangular lattice of dots, or on a grid with traceable lines between vertices. Some of the squares in the grid/matrix will have numbers inside them, dictating the number of line segments that border that space. The objective is to create an enclosed loop that satisfies the border requirements set out by the numbered spaces.
There are not many variations, as the primary method of changing the way the puzzle is solved is by changing the shape or size of the grid, as any planar graph can be used in place of a simple rectangular matrix/grid.
