M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Topological Indices on Line Graphs of Multi Wheel Graphs and Multi Prism Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Zeeshan Anwar; FA19-RMT-078; LHR TP 7413; Dr. Imran Zulfiqar CheemaTopological index is a numerical quantity which characterizes the whole structure of a graph. These indices are invariants under the graph isomorphism which characterizes its topology and are usually hold mathematical properties of graph invariant. Related to chemistry, actually it is a numerical quantity linked with chemical structure express for the relationship of chemical network with various physical-chemical characteristics like temperature, boiling points and path number etc. Actually these topological indices are formulated by transforming a chemical structure into a numeric number. In the area of research graph theory has been found to be very beneficial. In this thesis, we will calculate the degree based topological indices so-called Randic index, atom bond connectivity (ABC) index, geometric arithmetic(GA) index, first and second Zagreb, second modified Zagreb, third Zagreb, hyper Zagreb, Harmonic index, F-index, Shigehalli and Kanubar index for line graph of multi-wheel graph 𝑊𝑚 = (𝐶𝑛 × 𝑃𝑚) where 𝑚 ≥ 2 as well as line graph of multi-prism graph 𝑌𝑚,𝑛 = (𝐶𝑚 × 𝑃𝑛) where 𝑛 ≥ 4. We will also calculate degree sum based topological indices ABC₄ index known as the forth version of atom bond connectivity (ABC) index and GA₅ index which is the fifth class of geometric arithmetic (GA) index for these graphs. This study will give us a very interesting and different results by using new topological index that is first Zagreb and second Zagreb, second modified Zagreb, third Zagreb, hyper and augmented Zagreb topological indices.Item Weighted Mean Product of Certain Fuzzy Graph Structures(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Tariq Mehmood; FA19-RMT-044; LHR TP 7353; Dr. Imran Zulfiqar CheemaFuzzy set theory and fuzzy logics are examples of fuzzy mathematics. It began in 1965, when Lotfi Asker Zadeh's important work Fuzzy sets was issued. Fuzzy Graph theory is becoming very popular these days, so it is used in many major fields. In this thesis, by means of weighted mean fuzzy transitivity here also I want to define for understanding (weighted mean transitivity) Weighted mean transitivity is defined as: μ(u,v) ≤ λ(σ(u)∨σ(v))+(1-λ)(σ(u)∧σ(v)) u₁,u₂∈ Ri′ where λ is optimized parameter and λ∈[0,1]. Now here we check λ at different values of interval. We discuss the different graph structure at λ=0, 0.5, 1. But here only we discuss λ= 0.5, 1. We calculate the Semi Strong min-product on different structures, degree of a vertex and total degree of a vertex. At the end of thesis we write the application as well as Algorithm.