Component edge connectivity and extra edge connectivity of alternating group networks

The l-component edge connectivity of a graph G, denoted by cAl(G), is the minimum number of edges whose removal from G results in a disconnected graph with at least l-components. The h-extra edge connectivity of a graph G, denoted by ?(h)(G), is the minimum number of edges whose removal from G results in a disconnected graph and each component has at least h + 1 vertices. In this paper, we determine the l-component edge connectivity and the h-extra edge connectivity of alternating group networks for some small values. For l-component edge connectivity, we prove that c?(3)(AN(n)) = 2n - 3 for n = 3, c?(4)(AN(n)) = 3n - 6 for n = 4, and c?(5)(AN(n)) = 4n - 8 for n = 4. For h-extra edge connectivity, we prove that ?(1)(AN(n)) = 2n - 4, ?(2)(AN(n)) = 3n - 9 and ?(3)(AN(n)) = 4n - 12 for n = 6.