Pancyclic and panconnected line graphs
Abdelhamid Benhocine, Jean‐Luc Fouquet · Journal of Graph Theory · 1987
Abstract Let G be a graph of order n ⩾ 3. We prove that if G is k‐connected (k ⩾ 2) and the degree sum of k + 1 mutually independent vertices of G is greater than 1/3(k + 1)(n + 1), then the line graph L(G) of G is pancyclic. We also prove that if G is such that the degree sum of every 2 adjacent vertices is at least n, then L(G) is panconnected with some exceptions.