AreebFA14-MSMATH-009LHR TP 6935Dr. Sana Javed2026-03-122016https://repository.cuilahore.edu.pk/handle/123456789/2723In this thesis, various chromatically unique and correspondent pairs of several families of graphs with same girths have been attained. Subdivided complete graphs are related to these families, indeed. Our major goal in this paper is to carry on the study of chromaticity of the subdivided complete graphs. We are dealing particularly with four vertices which is called 𝑘4-homeomorph. Distinctiveness of two particular classes of 𝑘4-homeomorph graphs with girth 11 has been explained in detail. The cycles of different lengths from graph has been removed during the discussion. In order to make them chromatically unique, vital and satisfactory conditions have been established. All well known definitions, results and terms are given in Chapter 1. Chapter 2 is covering a brief literature review about chromatic uniqueness and correspondence. While the chapter 3 is focused on the chromatic uniqueness along with chromatic equivalence of two 𝐾4-homeomorph graphs with same girth. At the end of the thesis, few open problems have been recommended as well.enDr. Sana JavedFA14Department of MathematicsMathematicsMATHEMATICSThesis