Connectivity of iterated line graphs
Discrete Applied Mathematics
Graph Theory With Applications
Graph Theory With Applications
Iterated open neighborhood graphs and generalizations
Discrete Applied Mathematics
On average connectivity of the strong product of graphs
Discrete Applied Mathematics
Spanning 3-connected index of graphs
Journal of Combinatorial Optimization
| Hi-index | 0.04 |
Let k=0 be an integer and L^k(G) be the kth iterated line graph of a graph G. Niepel and Knor proved that if G is a 4-connected graph, then @k(L^2(G))=4@d(G)-6. We show that the connectivity of G can be relaxed. In fact, we prove in this note that if G is an essentially 4-edge-connected and 3-connected graph, then @k(L^2(G))=4@d(G)-6. Similar bounds are obtained for essentially 4-edge-connected and 2-connected (1-connected) graphs.