A new approach to the study of fixed points based on soft rough covering graphs

Abstract

<abstract><p>Mathematical approaches to structure model problems have a significant role in expanding our knowledge in our routine life circumstances. To put them into practice, the right formulation, method, systematic representation, and formulation are needed. The purpose of introducing soft graphs is to discretize these fundamental mathematical ideas, which are inherently continuous, and to provide new tools for applying mathematical analysis technology to real-world applications including imperfect and inexact data or uncertainty. Soft rough covering models $ \left(\text{briefly}, \text{ }\mathcal{SRC}\text{-Models}\right) $, a novel theory that addresses uncertainty. In this present paper, we have introduced two new concepts $ \mathcal{L}\mathfrak{i} $-soft rough covering graphs ($ \mathcal{L}\mathfrak{i} $-$ \mathcal{SRCG} $s) and the concept of fixed point of such graphs. Furthermore, we looked into a some algebras that dealt with the fixed points of $ \mathcal{L}\mathfrak{i} $-$ \mathcal{SRCG} $s. Applications of the algebraic structures available in covering soft sets to soft graphs may reveal new facets of graph theory.</p></abstract>