Browsing by Author "Bacha Khan"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Comparative analysis of proper edge coloring of direct product of path and star fuzzy graphs
    (UMT Lahore, 2025-02-12) Bacha Khan
    This paper discovers the study of adjacent vertex distinguishing proper edge coloring (AVDPEC) in the context of direct product of fuzzy graphs, with a particular prominence on fuzzy path and fuzzy star graph combinations. In this study, we apply the classical coloring theory of crisp graphs to fuzzy graphs, as membership values add a subtle layer of intricacy to them. In circumstances where system elements are not unconditionally binary, this nuanced method allows us to describe and examine complex systems that call for a certain amount of vagueness or partial membership. We start with a detailed explanation of the essential concepts of graph coloring for both crisp and fuzzy graphs, along with an introduction to the novel fuzzy graph classes that result from this research. Our key contribution comprises an algorithm for the direct product of fuzzy path and fuzzy star networks, which acquires appropriate edge coloring that separates adjacent vertices utilizing fuzzy membership values. There are four main steps in the proposed coloring algorithm. The first step is to pick the color that matches the edge with the lowest membership value in either 𝑃𝑚 or 𝑆𝑛. Step two comprises relocating consideration on the edges that are incident to vertices from both 𝑃𝑚 and 𝑆𝑛. The color of the edge that has the lowest membership value that arises on these vertices is elected in this case. Reallocating colors to edges that have previously been utilized in the direct product is the focus of the third step. Any remaining edges in the direct product that do not yet have a color allocated to them are given new colors in the fourth and final step. In applications where recognizing between entities or tasks is crucial, this algorithm pursues to guarantee that each adjacent vertex pair in the fuzzy graph product is recognized by the particular colors of their incident edges. In order to highlight how changes in membership values affect the coloring procedure, we suggested expressive examples that show how the algorithm works with both crisp and fuzzy graphs. We determine a number of new characteristics and behaviors particular to fuzzy graph structures as an outcome of our exploration. The proper edge coloring in parallel computing guarantees negligible interference and effective source use by enhancing the assignment of computational jobs.
  • Thumbnail Image
    Item
    Practical application of linear algebra in animation using blender software
    (UMT Lahore, 2021) Bacha Khan
    Blender software is one the best innovation and creations of the 21st century, even a daydreaming project which cannot be pinned down easily, is be made through this blender software by employing its different features. It is endowed with the most attractive features including 3D visualizations, 3D animation, VFX shorts, Video Editing, Modelling, Rigging, compositing, texturing, rendering and simulations. In this project, the author employed the blender software for the purpose of physically constructing an animated car over a bridge by giving background and the surroundings were well decorated through different features of the blend, which was the dire need of my project and also employing blender kit through the designing phase. This is what gives us the aspiration to animate the car, decorate the bridge, and design street lamps. As a result, the author finally animated the car over the bridge, which took around eight seconds to complete its departure from the starting point. This project is an attempt to explain the facets of an animated car step by step in the following chapters.