A graph G is weakly 4-connected if it is 3-connected, has at least five vertices, and for every pair (A,B) such that A ∪ B = V (G), |A ∩ B| = 3 and no edge has one end in A − B and the other in B − A, one of the induced subgraphs G[A], G[B] has at most four edges. We describe a set of constructions that starting from a weakly 4-connected planar graph G produce a finite list of non-planar weakly...

Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G \ v. Denote the algebraic connectivities of G and G \ v by α(G) and α(G \ v), respectively. In this paper, we consider the functions φ(v) = α(G) − α(G \ v) and κ(v) = α(G\v) α(G) , provide attainable upper and lower bounds on both functions, and characterise the equality ...

The 5G demonstrations in a business has significant role today's fast-moving technology. Manet 5G, drives wireless system intended at an enormously high data rate, lower energy, low latency, and cost. For this reason, routing protocols of MANET have the possibility being fundamentally flexible, performance, energy-efficient. communication aims to afford higher rates significantly Over-The-Air l...

Introduction: Mental arithmetic analysis based on Electroencephalogram (EEG) signal for monitoring the state of the user’s brain functioning can be helpful for understanding some psychological disorders such as attention deficit hyperactivity disorder, autism spectrum disorder, or dyscalculia where the difficulty in learning or understanding the arithmetic exists. Most mental arithmetic recogni...

Introduction: Medial temporal sclerosis (MTS) is a form of mesial temporal lobe epilepsy (mTLE). It is typically characterized by structural alterations in hippocampus (HC) and related mesial temporal lobe (MTL) network. Resting state functional connectivity (RSFC) is considered an ideal technique in quantifying the dysfunction and maladaptation in MTL network. It is well- dem...

This study aims at developing a fuzzy approach for the educational grading systems. Through this logic-based card is suggested. The system based on crisp just deals with numbers. Fuzziness, being an important property of language, motivates us to work and in environment. Before discussing actual grade some introduction about key concepts given readers. We have also analyzed difference evaluatin...

In the realm of linking networks to real world, connectivity (strength connectedness) plays a crucial role. this article, we introduce three types vertices based on indegree and outdegree directed rough fuzzy (DRFNs). We also define concept strength-reducing sets ( $$\mathcal {SRS}s$$ ) DRF-vertices, DRF-edges, important related results using strongest path in graphs (DRFGs). generalize idea Me...

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.

The increased demand of Wireless Sensor Networks (WSNs) in different areas of application have intensified studies dedicated to the deployment of sensor nodes in recent past. For deployment of sensor nodes some of the key objectives that need to be satisfied are coverage of the area to be monitored, net energy consumed by the WSN, lifetime of the network, and connectivity and number of deployed...