Neighbor Connectivity of Line Graphs
Zhao Zhang · Shinjang dashösi ilmiy jurnili · 2009
In this paper,we study the relationship between the edge neighbor connectivityλ_(NB) of agraph G and the(vertex) neighbor connectivityκ_(NB) of its line graph L(G),and prove thatλ_(NB)(G)≤κ_(NB)(L(G)).We also propose a new concept of restricted edge neighbor connectivityλ_(NB)~τ(G),and provethatκ_(NB)(L(G))≤λ_(NB)~τ(G).Then we study the problem of when the equalities hold.