Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.

The eccentric connectivity index ξ is a distance–based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. We prove that the broom has maximum ξ among trees with a fixed maximum vertex degree, and characterize such trees with minimum ξ . In addition, we propose a simple linear algorithm for calculating ξ of trees.

We have sampled the artist social network of Myspace and to it applied the pairwise relational connectivity measure Minimum cut/Maximum flow. These values are then compared to a pairwise acoustic Earth Mover’s Distance measure and the relationship is discussed. Further, a means of constructing playlists using the maximum flow value to exploit both the social and acoustic distances is realized.

For a graph G of order n, the maximum nullity of G is defined to be the largest possible nullity over all real symmetric n × n matrices A whose (i, j)th entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity and the related parameter minimum rank of the same set of matrices have been studied extensively. A new parameter, generic maximum nullity, is ...

2This paper describes a novel method for estimating the sparse dynamical model of neural functional connectivity. This method combines the group Lasso and Laguerre expansion techniques to achieve model sparsity. It has been applied to the identification of neural functional connectivity of hippocampal CA3-CA1. Results show that the sparse model out-performs the full model estimated with the sta...

In telecommunication networks, full connectivity resilience to multiple link failures is too costly as it requires a network topology with many redundant links. Alternatively, the of telecommunications can be improved by resorting available third-party networks for temporary additional until failing links are restored. this approach, some nodes must selected in advance act gateway when failure ...

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.