The connectivity index wα(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where α is a real number (α 6= 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T ). Also, for −1 ≤ α < 0, we give a sharp lower bound and a upper bound for wα(T ).

The Wiener index W (G) of a connected graph G is defined to be the sum

Dynamic connectivity networks identify directed interregional interactions between modeled brain regions in neuroimaging. However, problems arise when the regions involved in a task and their interconnections are not fully known a priori. Objective measures of model adequacy are necessary to validate such models. We present a connectivity formalism, the Switching Linear Dynamic System (SLDS), t...

Let G be a graph and δv the degree of its vertex v . The connectivity index of G is χ = ∑ (δu δv) −1/2 , with the summation ranging over all pairs of adjacent vertices of G . We offer a simple proof that (a) among n-vertex graphs without isolated vertices, the star has minimal χvalue, and (b) among n-vertex graphs, the graphs in which all components are regular of non–zero degree have maximal (...

background: the association of metabolic syndrome (ms) with left  ventricular (lv) hypertrophy is controversial. the objective of our study was to investigate the infl uence of ms on lv mass and geometry in community-based hypertensive patients among han chinese.materials and methods: this study included 1733 metabolic syndrome patients according to the international diabetes federation (idf) d...

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randić connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of v...

Left ventricular (LV) hypertrophy is an important predictor of morbidity and mortality in hypertensive patients, and its geometric pattern is a useful determinant of severity and prognosis of heart disease. Studies on LV geometric pattern involving large number of Nigerian hypertensive patients are limited. We examined the LV geometric pattern in hypertensive patients seen in our echocardiograp...

conclusions the findings suggest that estrogen supplementation increases damage in testicular tissue due to eccentric exercise. results conventional light microscopic results revealed that testes tissues of the eccentric exercise administered group and the estrogen supplemented group exhibited slight impairment. in groups that were both eccentrically exercised and estrogen supplemented, more de...