The family of all independent k-sets a graph containing fixed vertex v is called star and its center. Stars are interesting for their relation to Erdős–Ko–Rado graphs. Hurlbert Kamat conjectured that in trees the largest stars centered leaves. This conjecture was disproven independently by Baber, Borg, Feghali, Johnson, Thomas. In this paper we introduce tool bound size at certain vertices We u...

The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpill...

Insects cannot synthesize sterols de novo, so they typically require a dietary source. Cholesterol is the dominant sterol in most insects, but because plants contain only small amounts of cholesterol, plant-feeding insects generate most of their cholesterol by metabolizing plant sterols. Plants almost always contain mixtures of different sterols, but some are not readily metabolized to choleste...

We describe three new species of Trigonospila Pokorny (Tachinidae: Blondeliini) from Area de Conservación Guanacaste (ACG), northwestern Costa Rica. All were reared from -various species of ACG caterpillars during an ongoing inventory of caterpillars, their food plants and their parasitoids in dry forest, rain forest and cloud forest. By coupling morphology, photographic documentation, life his...

Among the phytophagous insects which attack crops, the fall armyworm, Spodoptera frugiperda (J.E. Smith, 1797) (Lepidoptera, Noctuidae) is particularly harmful in the initial growth phase of rice plants. As a potential means of controlling this pest, and considering that the entomopathogen Bacillus thuringiensis Berliner demonstrates toxicity due to synthesis of the Cry protein, the present stu...

Alike the little mouse of the Gruffalo's tale, many harmless preys use intimidating deceptive signals as anti-predator strategies. For example, several caterpillars display eyespots and face-like colour patterns that are thought to mimic the face of snakes as deterrents to insectivorous birds. We develop a theoretical model to investigate the hypothesis that these defensive strategies exploit a...