Note on vertex and total proper connection numbers. Issue 2 (1st August 2016) - Chizmar, Emily; Magnant, Colton; Salehi Nowbandegani, Pouria
Abstract: This note introduces the vertex proper connection number of a graph and provides a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper connection number and the vertex and edge proper connection numbers.