A graph 
whose line graph is 
is called the root graph 
of 
. In order words, 
. The root graph of a connected
graph is unique except for 
(the triangle graph),
which has root graphs 
and 
(the claw
graph) (Harary 1994, pp. 72-73).
Root Graph
See also
Line GraphExplore with Wolfram|Alpha
References
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Whitney, H. "Congruent Graphs and the Connectivity of Graphs." Amer. J. Math. 54, 150-168, 1932.Cite this as:
Weisstein, Eric W. "Root Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RootGraph.html