Stability Properties of Inclusive Connectivity for Graphs
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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This dissertation is an investigation of inclusive connectivity which is a localization of connectivity defined for each vertex and each edge of a graph. The inclusive edge vertex, mixed connectivity of a vertex v is the minimum number of edges vertices, graph elements whose removal yields a subgraph in which v is a cutvertex. All possible combinations of these three parameters with regard to edge addition stability, in which the value of the parameter will remain unchanged after the addition of any edge, is studied along with other various properties including a relationship between the stability of inclusive connectivity and global connectivity. A similar study in the stability for inclusive connectivity for edge deletion is conducted. Final topics include neutral edges, where a neutral edge is one whose removal does not change the respective inclusive connectivity value of any vertex, and inclusive connectivity stable graphs, where the sum of the respective inclusive connectivity values for all vertices remains the same no matter what edge is deleted.
- Theoretical Mathematics