Line graph

2020 Mathematics Subject Classification: Primary: 05C76 [MSN][ZBL]

of a graph $G$

The graph $L(G)$ having a vertex set in one-to-one correspondence with the edge set of $G$, and vertices adjacent in $L(G)$ if the corresponding edges in $G$ have exactly one vertex in common.

References

• Cvetković, Dragoš; Rowlinson, Peter; Simić, Slobodan Spectral generalizations of line graphs. On graphs with least eigenvalue $−2$ London Mathematical Society Lecture Note Series 314 Cambridge University Press(2004) ISBN 0-521-83663-8 Zbl 1061.05057