@article{De Ita_Bello López_Contreras González_2023, title={Extreme Topologies on Bipolygonal Graphs and Dinamic Trees}, volume={14}, url={https://ijcopi.org/ojs/article/view/335}, abstractNote={<p>We show how properties of the sequence β<sub>i,j</sub>, which represents the product between two Fibonacci’s numbers F<sub>i</sub> × F<sub>j</sub>, can be used for the computation of the Merrifield-Simmons index on bipolygonal graphs and trees.</p> <p>We show that the extreme values of the Merrifield-Simmons index on bipolygonal graphs are found in two consecutive columns of the table β<sub>i,j</sub> k=i+j=1,...,n. The minimum value in β<sub>3,k-3</sub> and the maximum value in β<sub>4,k-4</sub>.&nbsp; On the other hand we show that i(T<sub>n</sub> ∪ {v<sub>p</sub>, v }) is minimum when v is a new leaf node, and its father v<sub>p</sub> was also a leaf node in T<sub>n</sub>.</p> <p>Our methods does not require the explicit computation of the number of independent sets of the involved graphs. Instead, it is based on applying the edge and vertex division rules to decompose the initial graph.</p>}, number={1}, journal={International Journal of Combinatorial Optimization Problems and Informatics}, author={De Ita, Guillermo and Bello López, Pedro and Contreras González, Meliza}, year={2023}, month={Mar.}, pages={19–26} }