AKCE International Journal of Graphs and Combinatorics
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.
Chizmar, Emily C., Colton Magnant, Pouria Salehi Nowbandegani.
"Note on Vertex and Total Proper Connection Numbers."
AKCE International Journal of Graphs and Combinatorics, 13 (2): 103-106.
doi: 10.1016/j.akcej.2016.06.003 source: https://www.sciencedirect.com/science/article/pii/S0972860016300858?via%3Dihub