In wireless sensor and actor networks, Connectivity among actors is very important, especially in critical applications where actors collaborate with each other to provide a report as soon as possible. Sometimes a node failure divides the given network into several parts; causing loss of Connectivity between actors hence degrades the network performance. Several algorithms have been proposed to restore inter-actor Connectivity. In these methods, selecting appropriate failure handler to minimize the relocations is crucial. In this paper the issue of finding the best backup is supposed the same as finding shortest path in stochastic graph problem. Owing that the solving stochastic shortest path is NP-complete, DLA is used for failure handler choice. This essay also presents a hybrid algorithm named DLA-BuS for critical node Back Up Selection based on distributed learning automata. Here two methods are proposed; first one is that each actor node is equipped with a learning automaton so that their cooperation in learning process leads to select the desired backups. The second method states the presentation of DLA-MRF to repair stimulant failure of two adjacent actors. In order to show the performance of the proposed algorithms extensive simulations using Castalia simulator have been conducted. Simulation results demonstrate that the mentioned proposed algorithms outperform existing methods in terms of the number of nodes movement, total distance travels, the percentage of coverage reduction, and energy consumption.

Mobile sensor networks rely heavily on inter-sensor Connectivity for collection of data. Nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. A failure of a sensor leads to loss of Connectivity and may cause partitioning of the network into disjoint segments.A number of approaches have been recently proposed that pursue node relocation in order to restore Connectivity. DCR is a distributed partitioning detection and Connectivity Restoration algorithm to tolerate the failure of sensors. DCR proactively identifies sensors that are critical to the network Connectivity based on local topological information, and designates appropriate, preferably non-critical, backup nodes. Upon failure detection, the backup sensor initiates a recovery process that may involve coordinated relocation of multiple sensors. Here we proposed Energy aware Distributed partitioning detection and Connectivity Restoration al-gorithm (EDCR) that is an improvement of DCR algorithm. Therefore reducing the message exchange overhead, lower energy consumption, and thus will increase the network lifetime.

A topological index of a molecular graph G is a numeric quantity related to G which is invariant under symmetry properties of G. Let G be a molecular graph. The eccentric Connectivity index x(G) is defined as x(G)=åuÎV(G) deg(u) e (u), where deg (u) denotes the degree of vertex u in G and e (u) is the largest distance between u and any other vertex v of G. The augmented eccentric Connectivity index, Ax(G) is defined as Ax(G)=åuÎV(G) M(u)/e(u), where M (u) denotes the product of degrees of all neighbors of vertex u. In this paper, exact formulas for the eccentric Connectivity and augmented eccentric Connectivity indices of an infinite family of nanostar dendrimer are computed.

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Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topological characterization of graphs and in QSAR/QSPR studies.