Abstract
A polyomino system (sometimes referred as a square animal) is a finite 2-connected plane graph such that each interior face (also known as "cell") is surrounded by a regular square of side length one. In this paper, efficient formulae for calculating the Albertson index (also known as irregularity and third Zagreb index), total irregularity, Narumi-Katayama index and multiplicative Zagreb indices of polyomino chains (a type of polyomino system) are established, and extremal (maximal and minimal) polyomino chains with respect to the Albertson index, total irregularity and Narumi-Katayama index are characterized.