Soft Set Representations of First Barycentric Refinements of Simple Graphs

Shakir, Qays Rashid; Ali, Muhammad Irfan

doi:10.24271/psr.2025.516673.2088

Soft Set Representations of First Barycentric Refinements of Simple Graphs

Document Type : Original Article

Authors

Qays Rashid Shakir ¹

Muhammad Irfan Ali ²

¹ Information Technology Department, Technical College of Management, Baghdad, Middle Technical University, Baghdad, Iraq.

² Department of Mathematics, Islamabad Model College for Boys, Islamabad, Pakistan.

10.24271/psr.2025.516673.2088

Abstract

We investigate soft set representations of the first barycentric refinements of simple graphs. Simple graphs under consideration are those with cliques of size at most three. In such representations, we use soft sets to describe the first barycentric refinements of such simple graphs. We use the soft set representation of two graph operations to obtain the soft set representation of the first barycentric refinements of the graphs under consideration. Specifically, we deal with vertex-insertion and spider-insertion operations in terms of soft sets. Furthermore, we illustrate and investigate some properties of soft set representations of the first barycentric refinements of some special simple graphs.

Keywords

Simple graphs

graph operations

soft sets

soft set representations