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Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly
Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly
Electronic Theses and Dissertations
In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …
Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry
Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry
Electronic Theses and Dissertations
In a graph, the generalized distance between multiple vertices is the minimum number of edges in a connected subgraph that contains these vertices. When we consider such distances between all subsets of $k$ vertices and take the sum, it is called the Steiner $k$-Wiener index and has important applications in Chemical Graph Theory. In this thesis we consider the inverse problems related to the Steiner Wiener index, i.e. for what positive integers is there a graph with Steiner Wiener index of that value?