Connectivity and edge-connectivity of a graph measure the difficulty of breaking the graph apart, but they are very much affected by local aspects like vertex degree. Average connectivity (and analogously, average edge-connectivity) has been introduced to give a more refined measure of the global “amount” of connectivity. In this paper, we prove a relationship between the average connectivity a...

In Quantum Information Theory there is a construction for quantum channels, appropriately called graph, that generalizes the confusability graph classical channels in information theory. this paper definition of connectedness graphs provided, which definition. It shown several examples well-known (quantum Hamming cubes and expanders) are connected. A version particular case tree-packing theorem...

Generalized connectivity introduced by Hager (1985) has been studied extensively in undirected graphs and become an established area in undirected graph theory. For connectivity problems, directed graphs can be considered as generalizations of undirected graphs. In this paper, we introduce a natural extension of generalized k-connectivity of undirected graphs to directed graphs (we call it stro...