Combinatorial aspects of the L ö wenstein avoidance rule. Part I: the independence polynomial

This article and a companion paper deal with practical issues regarding the calculation of the independence ratio of mainly 2-periodic nets and the determination of site distributions realizing this ratio. The first paper describes a calculation technique based on propositional calculus and introduces a multivariate polynomial, called the independence polynomial. This polynomial can be calculated in an automatic way and provides the list of all maximal independent sets of the graph, hence also the value of its independence ratio. Some properties of this polynomial are discussed; the independence polynomials of some simple graphs, such as short paths or cycles, are determined as examples of calculation techniques. The method is also applied to the determination of the independence ratio of the 2-periodic net dhc.

Source: Acta Crystallographica Section A - September 24, 2021 Category: Chemistry Authors: Moreira de Oliveira Jr, M. Eon, J.-G. Tags: nets quotient graphs independence quotient research papers Source Type: research