Geodesic
Uniquely Line Colorable Graphs
Canadian mathematical bulletin, Tome 16 (1973) no. 4, pp. 525-529

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DOI

A line-coloring of a graph G is an assignment of colors to the lines of G so that adjacent lines are colored differently; an n-line coloring uses n colors. The line-chromatic number χ'(G) is the smallest n for which G admits an n-line coloring. 
Greenwell, D. L.; Kronk, H. V. Uniquely Line Colorable Graphs. Canadian mathematical bulletin, Tome 16 (1973) no. 4, pp. 525-529. doi: 10.4153/CMB-1973-086-2
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     title = {Uniquely {Line} {Colorable} {Graphs}},
     journal = {Canadian mathematical bulletin},
     pages = {525--529},
     year = {1973},
     volume = {16},
     number = {4},
     doi = {10.4153/CMB-1973-086-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-086-2/}
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