The maximum average connectivity among all orientations of a graph

Shattering, Graph Orientations, and Connectivity

We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied concepts of graph theory related to connectivity, combinatorial optimization, forbidden subgraphs, and others. In one direction, we use this connection to derive...

Toughness of the Networks with Maximum Connectivity

The stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. As the network begins losing links or nodes, eventually there is a loss in its effectiveness. Thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible...

The Maximum Number of Edges in a Strongly Multiplicative Graph

A note on "Tenacity of a graph with maximum connectivity"

In this note, we show that one of the arguments used by Moazzami for computing the tenacity of the third Harary graph is wrong and then improve the proof. © 2014 Published by Elsevier B.V.

toughness of the networks with maximum connectivity

the stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. as the network begins losing links or nodes, eventually there is a loss in its effectiveness. thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible...