Path connectivity of line graphs

Abstract

Dirac showed that in a $(k-1)$-connected graph there is a path through each $k$ vertices. The path $k$-connectivity $\ddot{I}{€}_k(G)$ of a graph $G$, which is a generalization of Dirac's notion, was introduced by Hager in 1986. In this paper, we study path connectivity of line graphs.

15 pages. arXiv admin note: substantial text overlap with arXiv:1508.07202, arXiv:1207.1838; text overlap with arXiv:1103.6095 by other authors