Formulation, Proposition and Application of Interval Semigraph

Abstract

Semigraph represents a versatile extension within graph theory, offering a broader framework for exploration. Among these, intersection graphs hold pivotal roles, serving as essential analytical tools with wide-ranging applications. In this study, we introduce the integration of intersection graphs into the generalized structure of semigraphs, aiming to invigorate researchers’ interest and encourage further advancements in this domain. This paper introduces two novel concepts: edge intersection semigraphs and interval semigraphs. Additionally, foundational results pertaining to these concepts are established, elucidating their fundamental properties. Furthermore, we illustrate the practical utility of interval semigraphs through an illustrative example involving their application in optimizing road traffic management systems.