Operations on Fuzzy Incidence Graphs and Strong Incidence Domination

TL;DR

This paper explores operations on fuzzy incidence graphs, focusing on strong fuzzy incidence graphs, and investigates properties, bounds, and domination concepts within these graph structures.

Contribution

It introduces and analyzes operations on fuzzy incidence graphs, especially strong variants, and studies their domination properties and bounds.

Findings

Bounds for domination number in product graphs are established.

Properties of FIGs under various operations are characterized.

Strong incidence domination number is examined in different graph operations.

Abstract

Fuzzy incidence graphs (FIG) model real world problems efficiently when there is an extra attribute of vertex-edge relationship. The article discusses the operations on Fuzzy incidence graphs. The join, Cartesian product, tensor product, and composition of FIGs are explored. The study is concentrated mainly on strong fuzzy incidence graphs (SFIG). The idea of strong incidence domination (SID) is used, and strong incidence domination number (SIDN) in operations is examined. Basic properties of FIGs obtained from the operations are studied. Bounds for the domination number of product of two SFIGs are determined for the Cartesian and tensor products. Study is conducted on FIGs with strong join and composition. Complete fuzzy incidence graphs (CFIGs) and FIGs with effective pairs are also considered in the study.