Reduction Criteria for Extremal Degree-Based Indices of General Polyomino Chains

This paper establishes reduction criteria for extremal problems of degree-based indices on generalpolyomino chains. These criteria identify conditions under which the optimization over generalpolyomino chains can be reduced to the restricted polyomino-chain setting, allowing the use of asimpler dynamic programming framework. As a main application, we characterize, for any fixednumber of squares, the general polyomino chains that minimize the generalized Randić index forα ≤−1.23853 and maximize it for α ≤ −1.56204.