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 ...

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...

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.

Background: Tinnitus known as a central nervous system disorder is correlated with specific oscillatory activities within auditory and non-auditory brain areas. Several studies in the past few years have revealed that in the most tinnitus cases, the response pattern of neurons in auditory system is changed due to auditory deafferentation, which leads to variation and disruption of the brain net...

In this paper we introduce $(alpha,beta)-$linear connected spaces for nonzero cardinal numbers $alpha$ and $beta$. We show that $(alpha,beta)-$linear connectivity approach is a tool to classify the class of all linear connected spaces.

In this paper, we calculate the eccentric connectivity index and the eccentricity sequence of two infinite classes of fullerenes with 50 + 10k and 60 + 12k (k in N) carbon atoms.