Line‐graphical degree sequences
Douglas Bauer · Journal of Graph Theory · 1980
Abstract A degree sequence π = (d1, d2,…,dp), with d1 ≥ d2 ≥…≥ dp, is line graphical if it is realized by the line graph of some graph. Degree sequences with line‐graphical realizations are characterized for the cases d1 = p ‐ 1, d1 = p ‐ 2, d1 ≤ 3, and d1 = dp. It is also shown that if a degree sequence with d1 = p‐1 is line graphical, it is uniquely line graphical. It follows that with possibly one exception each line‐graphical realization of an arbitrary degree sequence must have either C5, 2K1, + K2, K1 + 2K2, or 3K1, as an induced subgraph.