The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the connectivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1(L) = 2λ1(D), and that for a connected graph G and its line graph L, if one of κ1(L) and λ2(G) exists, then κ1...

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

Staying attached at a favorable site can be a major challenge for organisms in flow. Meeting this challenge depends on properties of the attachment structure and substrate, the nature of fluid flow, and the ability to adjust attachment force in response to hydrodynamic conditions. A broad taxonomic range of adult stages use adhesion or suction to attach to hard substrates in intertidal habitats...

In communication networks, greater degrees of stability or less vulnerability is required. The vulnerability of communication network measures the resistance of the network to the disruption of operation after the failure of certain stations or communication links. If the network begins losing communication links or processors, then there is a loss in its effectiveness. Thus, communication netw...

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.