Faisal JavedSP19-RMT-036LHR TP 7348Dr. Muhammad Hussain2026-03-132021https://repository.cuilahore.edu.pk/handle/123456789/2799The graph ? consists of some vertex ?(?) are connected by ?(?) where the position of vertices does not matter. The degree of a graph vertex is basically a number of incident edges ?(?) and vertex ? can be denoted by du. The upper and lower bound of graph energy with minimal and maximal energy is abroad field of Spectral Graph theory. The energy of Graph ?(?) in term of vertices and number of edges in graph ? is involved in absolute value of eigenvalue adjacency matrix of G where λ is the spectral radius. The Graph has energy equal to ?(?) = ∑ |? ? ?=1 |. An irregular graph G is totally defined as ??𝑡(?) = |𝑢 − 𝑣|. Finally, we determine the energy, pattern and irregularities of chain like cyclic graph. Our exploring outputs will rely upon Size and Order of Graph, Degree of Graph, Irregular Graph, Multi Graph, Cyclic Graph, Wheel Graph, Bridge Graph, Prism Graph, Connected and Planarity Graph, and Concept of Distance and Degree in Graph.enDr. Muhammad Hussainsp19Department of MathematicsMathematicsThesis