The Second Isoperimetric Connectivityof Line Graphs and Line Digraphs
Jixiang Meng · Shinjang dashösi ilmiy jurnili · 2006
In this paper,we show that the second isoperimetric connectivity of strongly connected line digraphs with \$δ≥\$ equals its connectivity.For line graphs,we give a sufficient and necessary condition for the existence of the second isoperimetric connectivity,and we show that under the condition that the second isoperimetric connectivity exists,the second isoperimetric connectivity equals either the restricted vertex connectivity or \$d_1+d_2\$,where \$d_1\$ and \$d_2\$ are the smallest and the second smallest degree respectively.