We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...

nonspecific activity-related arm pain is characterized by an absence of objective physical findings and symptoms that do not correspond with objective pathophysiology. arm pain without strict diagnosis is often related to activity, work-related activity in particular, and is often seen in patients with physically demanding work. psychological factors such as catastrophic thinking, symptoms of d...

Irradiation of pyran-2-ones bearing pendent furans in aqueous MeOH followed by heating furnished fused bicyclic products containing a cyclooctatriene ring.

the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...

Abstract The Heliconia species with pendent inflorescences and colorful bracts are a good option as cut flower for floriculture market, but only few of this type eg. H. rostrata, rauliniana chartacea commercially produced in Brazil. This study was carried out to characterize 36 accessions, inflorescences, be used flower, intending increase knowledge use these exceptional plants among tropical e...