Radius and subpancyclicity in line graphs Original Research Article

A graph is called subpancyclic if it contains cycles of length from 3 to its circumference. Let image be a graph with image. In this paper, we prove that if one of the following holds: the radius of image is at most image; image has no subgraph isomorphic to image; the circumference of image is at most image; the length of a longest path is at most image, then the line graph image is subpancyclic and these conditions are all best possible even under the condition that image is hamiltonian.