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Note On Vertex And Total Proper Connection Numbers, Emily C. Chizmar, Colton Magnant, Pouria Salehi Nowbandegani
Note On Vertex And Total Proper Connection Numbers, Emily C. Chizmar, Colton Magnant, Pouria Salehi Nowbandegani
Department of Mathematical Sciences Faculty Publications
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.
Directed Proper Connection Of Graphs, Colton Magnant, Patrick R. Morley, Sarabeth A. Porter, Pouria Salehi Nowbandegani, Hua Wang
Directed Proper Connection Of Graphs, Colton Magnant, Patrick R. Morley, Sarabeth A. Porter, Pouria Salehi Nowbandegani, Hua Wang
Department of Mathematical Sciences Faculty Publications
An edge-colored directed graph is called properly connected if, between every pair of vertices, there is a properly colored directed path. We study some conditions on directed graphs which guarantee the existence of a coloring that is properly connected. We also study conditions on a colored directed graph which guarantee that the coloring is properly connected.