The algebraic connectivity of a graph, which is the second-smallest eigenvalue of the Laplacian of the graph, is a measure of connectivity. We show that the problem of adding a specified number of edges to an input graph to maximize the algebraic connectivity of the augmented graph is NP-hard.

background: the aim of this study was to investigate muscle damage indicators and electromyography activities of quadriceps muscles at 25° of hip flexion in untrained healthy females after an eccentric exercise induced muscle fiber damage.   methods : a total of 14 healthy females participated in this pre-experimental study. the subjects performed maximal eccentric quadriceps contractions at 25...

Let $G=(V,E)$ be a simple connectedgraph with $n$ vertices, $m$ edges and sequence of vertex degrees$d_1 ge d_2 ge cdots ge d_n>0$, $d_i=d(v_i)$, where $v_iin V$. With $isim j$ we denote adjacency ofvertices $v_i$ and $v_j$. The generalsum--connectivity index of graph is defined as $chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}$, where $alpha$ is an arbitrary real<b...

The adjacent eccentric distance sum index of a graph G is defined as ξsv(G) = ∑ v∈V (G) ε(v)D(v) deg(v) , where ε(v), deg(v) denote the eccentricity, the degree of the vertex v, respectively, and D(v) = ∑ u∈V (G) d(u, v) is the sum of all distances from the vertex v. In this paper we derive some upper or lower bounds for the adjacent eccentric distance sum in terms of some graph invariants or t...

BACKGROUND AND PURPOSE Eccentric stenosis of the coronary artery is associated with plaque disruption and acute coronary syndrome. The purpose of the present study was to determine whether eccentric stenosis of the carotid artery contributes to cerebrovascular events. MATERIALS AND METHODS Of 6859 patients with vascular diseases who underwent duplex carotid ultrasonography, we studied 512 int...

Connectivity is an important measurement for the fault tolerance in interconnection networks. It is known that the augmented cube AQn is maximally connected, i.e. (2n − 1)-connected, for n ≥ 4. By the classical Menger’s Theorem, every pair of vertices in AQn is connected by 2n − 1 vertex-disjoint paths for n ≥ 4. A routing with parallel paths can speed up transfers of large amounts of data and ...

The augmented cube AQn, proposed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71–84], is a (2n− 1)-regular (2n− 1)-connected graph (n = 3). This paper determines that the super connectivity of AQn is 4n− 8 for n 6 and the super edge-connectivity is 4n− 4 for n 5. That is, for n 6 (respectively, n 5), at least 4n− 8 vertices (respectively, 4n− 4 edges...