Proper Connection Of Direct Products

Richard H. Hammack, and Dewey T. Taylor. "Proper Connection Of Direct Products." Discussiones Mathematicae Graph Theory 37.4 (2017): 1005-1013. <http://eudml.org/doc/288458>.

@article{RichardH2017,
abstract = {The proper connection number of a graph is the least integer k for which the graph has an edge coloring with k colors, with the property that any two vertices are joined by a properly colored path. We prove that given two connected non-bipartite graphs, one of which is (vertex) 2-connected, the proper connection number of their direct product is 2.},
author = {Richard H. Hammack, Dewey T. Taylor},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {direct product of graphs; proper connection of graphs.},
language = {eng},
number = {4},
pages = {1005-1013},
title = {Proper Connection Of Direct Products},
url = {http://eudml.org/doc/288458},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Richard H. Hammack
AU - Dewey T. Taylor
TI - Proper Connection Of Direct Products
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 4
SP - 1005
EP - 1013
AB - The proper connection number of a graph is the least integer k for which the graph has an edge coloring with k colors, with the property that any two vertices are joined by a properly colored path. We prove that given two connected non-bipartite graphs, one of which is (vertex) 2-connected, the proper connection number of their direct product is 2.
LA - eng
KW - direct product of graphs; proper connection of graphs.
UR - http://eudml.org/doc/288458
ER -