The additive hereditary property of linear forests is characterized by the existence of average labellings.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1046, author = {Mat\'u\v s Harminc}, title = {On a characterization of graphs by average labellings}, journal = {Discussiones Mathematicae Graph Theory}, volume = {17}, year = {1997}, pages = {133-136}, zbl = {0904.05076}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1046} }
Matúš Harminc. On a characterization of graphs by average labellings. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 133-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1046/
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