Annals of Communications in Mathematics

AbstractIn order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper we have presented how partially ordered sets can be studied under simultaneous partially ordered relations which we have called binary posets. The paper is motivated by the problem of operating a set simultaneously under two distinct partially ordered relations. It has been shown that binary posets follow duality principle just like posets do. Within this framework, some new definitions concerning maximal and minimal elements are also presented. Furthermore, some theorems on order isomorphism and Galois connections are derived.

AbstractSoft graph theory offers a parametrized perspective on graphs by classifying the universe’s components according to a specified set of parameters. This paper explores soft graph theory, which classifies graph components based on a set of parameters, focusing on the wheel and friendship graph families. By analyzing soft graphs with distance-based parameter sets, the study provides key results on the isomorphic subgraphs formed within these structures. These findings offer important insights into the structure and behavior of soft graphs, enhancing our understanding of soft graph theory.