In this paper, we computed the Tutte polynomials of (2,n)-torus knots and introduced general formulas for this process. Firstly, we obtained the isomorphic graphs and dual graphs of (2,n)-torus knots from their regular diagrams. Then, we computed the Tutte polynomials by these graphs. Finally, we obtained that the Tutte polynomials of the isomorphic graphs and dual graphs of (2,n)-torus knots are equivalent to each other. Moreover we computed the Tutte polynomials for signed graphs, which their edges are each labelled with a sign {+1 or − 1}, of (2,n)-torus knots. we obtained two generalizations for these graphs.
Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space X is said to be scattered if every nonempty subset S of X contains at least one point which is isolated in S. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan-Gottesman compactification of T3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification X* is a scattered.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.