The Gutman index is a degree-distance-based topological descriptor of connected graphs. In this paper, we derive explicit analytic expressions for its expected value in polyomino chains built by sequentially attaching square tiles via one of two fixed local connection modes. This expectation is expressed as a cubic polynomial in the number of tiles $n$. We then identify which attachment patterns yield the extremal (maximum and minimum) values and compute the overall average of the Gutman index across all polyomino chains of length $n$. These results enhance the topological analysis of square-tiled networks with applications in chemical graph theory, polymer science, and materials design.
Azami, L. and Jafari Rad, N. (2025). Gutman index of polyomino chains. Journal of Discrete Mathematics and Its Applications, 10(4), 375-392. doi: 10.22061/jdma.2025.12559.1168
MLA
Azami, L. , and Jafari Rad, N. . "Gutman index of polyomino chains", Journal of Discrete Mathematics and Its Applications, 10, 4, 2025, 375-392. doi: 10.22061/jdma.2025.12559.1168
HARVARD
Azami, L., Jafari Rad, N. (2025). 'Gutman index of polyomino chains', Journal of Discrete Mathematics and Its Applications, 10(4), pp. 375-392. doi: 10.22061/jdma.2025.12559.1168
CHICAGO
L. Azami and N. Jafari Rad, "Gutman index of polyomino chains," Journal of Discrete Mathematics and Its Applications, 10 4 (2025): 375-392, doi: 10.22061/jdma.2025.12559.1168
VANCOUVER
Azami, L., Jafari Rad, N. Gutman index of polyomino chains. Journal of Discrete Mathematics and Its Applications, 2025; 10(4): 375-392. doi: 10.22061/jdma.2025.12559.1168
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