Let G be a simple non-complete graph of order n. The r-component edge connectivity of G denoted as λ r (G) is the minimum number of edges that must be removed from G in order to obtain a graph with (at least) r connected components. The concept of r-component edge connectivity generalizes that of edge connectivity by taking into account the number of components of the resulting graph. In this paper we establish bounds of the r component edge connectivity of an important family of interconnection network models, the generalized Petersen graphs GP(n, k) in which n and k are relatively prime integers.

Instructors often write feedback on students' proofs even if there is no expectation for the students to revise and resubmit the work. It is not known, however, what students do with that feedback or if they understand the professor's intentions. To this end, we asked eight advanced mathematics undergraduates to respond to professor comments on four written proofs by interpreting and implementing the comments. We analyzed the student's responses using the categories of corrective feedback for language acquisition, viewing the language of mathematical proof as a register of academic English.

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