This study was designed to investigate the inhibitory effect of Gynura procumbens extract against carbohydrate digesting enzymes and its ability to ameliorate postprandial hyperglycemia in streptozotocin (STZ)-induced diabetic mice. G. procumbens extract showed prominent α-glucosidase and α-amylase inhibitory effects. The half-maximal inhibitory concentration (IC50) of G. procumbens extract aga...

A stable set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is I(G;x) = s0+s1x+s2x 2 +...+sαx α , where α = α(G) is the cardinality of a maximum stable of G, while sk equals the number of stable sets of size k in G (Gutman and Harary, 1983). Hamidoune, 1990, showed that for every claw-free graph G (i.e., a graph having no induced subgraph isomorphic to...

We have seen that in any graph G = (V,E), a maximum-size matching can be found in polynomial time. This means that α(L(G)) can be found in polynomial time, where L(G) is the line graph of G.2 On the other hand, it is NP-complete to find a maximum-size stable set in a graph. That is, determining α(G) is NP-complete. Since α(G) = |V |−τ(G) and α(G) = ω(G), also determining the vertex cover number...

Throughout today’s lecture, we fix a connected graph G and a strict threshold weighting θ : E(G)→ [0, 2] (such that ∆θ(H) := |V (H)| − ∑ e∈E(H) θ(e) > 0 for all ∅ ⊂ H ⊂ G). Also throughout today’s lecture, let α be a uniform random element of [n]V (G) (independent of Xθ). We think of α as a random choice of vertices from each color class of G ↑n. For each subgraph H ⊆ G, we have the isomorphic ...

In this paper we construct a new type of q-Genocchi numbers and polynomials with weak weight α: G (α) n,q , G (α) n,q (x) respectively. Some interesting results and relationships are obtained.

We have seen that in any graph G = (V, E), a maximum-size matching can be found in polynomial time. This means that α(L(G)) can be found in polynomial time, where L(G) is the line graph of G.2 On the other hand, it is NP-complete to find a maximum-size stable set in a graph. That is, determining α(G) is NP-complete. Since α(G) = |V |−τ(G) and α(G) = ω(G), also determining the vertex cover numbe...

For a connected graph G of order n, the clique number ω(G), the chromatic number χ(G) and the independence number α(G) satisfy ω(G) ≤ χ(G) ≤ n − α(G) + 1. We will show that the arithmetic mean of the previous lower and upper bound provides a new upper bound for the chromatic number of a graph.

Let n(G) and α(G) be the order and the independence number of a graph G, repsectively. If G is bipartite graph, then it is well-known and easy to see that α(G) ≥ n(G) 2 . In this paper we present a constructive characterization of bipartite graphs G for which

Let G be a finite and simple graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If ∑ x∈N [v] f(x) ≤ 1 for each v ∈ V (G), where N [v] is the closed neighborhood of v, then f is a signed 2independence function onG. The weight of a signed 2-independence function f is w(f) = ∑ v∈V (G) f(v). The maximum of weights w(f), taken over all signed 2-independence functions ...