Extremal Matching Energy of Random Polyomino Chains

Abstract

Polyomino graphs is one of the research objectives in statistical physics and in modeling problems of surface chemistry. A random polyomino chain is a subgraph of a polyomino graph. The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. In this paper, we characterize the graphs with the extremal matching energy among all random polyomino chains of a polyomino graph by the probability method.

On degree–based topological indices of random polyomino chains

“…Continuing along the same vein, it is important to highlight that, the calculation of different topological indices, extreme problems, and exploring topics, such as perfect pairings, dimer covering and their connection with caterpillar trees, among others [30,31,32,33,34,35,36,37,38,39] are active investigations on chains of polyominoes and chains of random polyominoes.…”