Open AccessMathematical modeling of finite topologies
Author(s) -
Sayyed Ehsan Monabbati,
Hamid Torabi
Publication year - 2020
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.12.2.434-442
Subject(s) - network topology , mathematics , comparison of topologies , finite set , representation (politics) , set (abstract data type) , topology (electrical circuits) , integer programming , mathematical optimization , extension topology , general topology , discrete mathematics , combinatorics , computer science , topological space , mathematical analysis , politics , political science , law , programming language , operating system
Integer programming is a tool for solving some combinatorial optimization problems. In this paper, we deal with combinatorial optimization problems on finite topologies. We use the binary representation of the sets to characterize finite topologies as the solutions of a Boolean quadratic system. This system is used as a basic model for formulating other types of topologies (e.g. door topology and $T_0$-topology) and some combinatorial optimization problems on finite topologies. As an example of the proposed model, we found that the smallest number $m(k)$ for which the topology exists on an $m(k)$-elements set containing exactly $k$ open sets, for $k = 8$ and $k = 15$ is $3$ and $5$, respectively.