Relationship between extra edge connectivity and component edge connectivity for regular graphs.

• The ℓ -extra (resp. ℓ -component) edge connectivity λ (ℓ) (G) (resp. λ ℓ (G)) is a good measure of robustness for networks. • The relationship between ℓ -extra edge connectivity and (ℓ + 2)-component edge connectivity for regular graphs is given. • As applications, the extra edge connectivity and component edge connectivity are explored for some well-known networks. A conditional connectivity is the generalization of the traditional connectivity and can provide more accurate measures regarding the reliability of a large-scale multiprocessor system. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. Although these two measures have attracted considerable attention and been determined for many classes of graphs in recent years, they are established independently. In this paper, we determine the relationship between extra edge connectivities and component edge connectivities of regular networks. Using this relationship, the extra edge connectivity and component edge connectivity are explored for some well-known graphs, including BC graphs, data center networks, augmented k -ary n -cubes, hierarchical star networks, burnt pancake graphs, (n , k) -star graphs, etc. [ABSTRACT FROM AUTHOR]