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.

Functional MRI (fMRI) is an indirect measure of neural activity as a result of the convolution of the hemodynamic response function (HRF) and latent (unmeasured) neural activity. Recent studies have shown variability of HRF across brain regions (intra-subject spatial variability) and between subjects (inter-subject variability). Ignoring this HRF variability during data analysis could impair th...

While researchers have extensively characterized functional connectivity between brain regions, the characterization of functional homogeneity within a region of the brain connectome is in early stages of development. Several functional homogeneity measures were proposed previously, among which regional homogeneity (ReHo) was most widely used as a measure to characterize functional homogeneity ...

As the Internet represents a key social infrastructure, its reliability is essential if we are to survive failures. Physical connectivity of networks is also essential as it characterizes reliability. There are collaboration structures, which are topological structures where two or more nodes are connected to a node, and collaboration structures are observed in transcriptional regulatory networ...

In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.

In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.

An interconnection network system consists of layers of switching elements connected together in a predefined topology providing the connectivity between the set of processors and the set of memory modules. Performance analysis of a network system is important as it determines the usability and the efficiency of the network to provide services. A shuffle-exchange network (SEN), a specific type ...

A general assumption made in evaluation of flow network reliability is perfectly reliable nodes. Under such assumption, network reliability is evaluated through subset cut or composite path set approaches. This paper presents a simple approach to account for node failures in reliability evaluation of flow networks using subset cut approach. The proposed approach starts with generating combinati...