The connectivity indices concept of neutrosophic graph and their application of computer network, highway system and transport network flow

Abstract

To address information ambiguities, this study suggests using neutrosophic sets as a tactical tool. Three membership functions (called Tr,In,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_r, I_n, $$\\end{document} and Fi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ F_i$$\\end{document}) that indicate an object’s degree of truth, indeterminacy, and false membership constitute the neutrosophic set. It becomes clear that the neutrosophic connectivity index (CIN) is an essential tool for solving practical problems, especially those involving traffic network flow. To capture uncertainties, neutrosophic graphs are used to represent knowledge at different membership levels. Two types of CINs,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$CIN_s,$$\\end{document} mean CIN and CIN, are investigated within the framework of neutrosophic graphs. In the context of neutrosophic diagrams, certain node types-such as neutrosophic neutral nodes, neutrosophic connectivity reducing nodes (NCRN) , and neutrosophic graph connectivity enhancing nodes (NCEN) , play important roles. We concentrate on two types of networks, specifically traffic network flow, to illustrate the real-world uses of CIN. By comparing results, one can see how junction removal affects network connectivity using metrics like Connectivity Indexes (CIN) and Average Connectivity Indexes (ACIN) . A few nodes in particular, designated by ACIN as Non-Critical Removal Nodes (NCRNs)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ (NCRN_s) $$\\end{document}, show promise for increases in average connectivity following removal. To fully comprehend traffic network dynamics and make the best decisions, it is crucial to take into account both ACIN and CIN insights. This is because different junctions have different effects on average and overall connectivity metrics.