Browsing by Subject "graph, vertex"

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    Eccentricity-based fault tolerance in graphs
    (2026) Wade, Michael; Allie, Imran; Du Preez, Brandon
    The eccentricity of a vertex in a graph is the maximum length of a shortest path from that vertex to any other vertex in the graph. The eccentricity index of a graph is the sum of the eccentricities of the vertices in the graph. A fault in a graph is a vertex or edge deletion. In this thesis, we study eccentricity-based measures and properties of fault tolerance in graphs. Specifically, we study the change in the eccentricity of a vertex and the eccentricity index of a graph after edge or vertex deletions. We begin by discussing literature on edge-deleted eccentricity and edge-deleted eccentricity stable graphs. We then introduce vertex-deleted eccentricity and the average vertex-deleted eccentricity index of a graph and prove novel results regarding these concepts. Finally, we conclude by assessing the fault tolerance of common graphs in computer network design based on the measures discussed previously