Let G be a graph without isolated vertices and let α(G) be its stability number and τ(G) its covering number. The σv-cover number of a graph, denoted by σv(G), is the maximum natural number m such that every vertex of G belongs to a maximal independent set with at least m vertices. In the first part of this paper we prove that α(G) ≤ τ(G)[1 + α(G)− σv(G)]. We also discuss some conjectures analo...

LetD = (V (D), A(D)) be a digraph; a kernelN ofD is a set of verticesN ⊆ V (D) such that N is independent (for any x, y∈N there is no arc between them) and N is absorbent (for each x ∈ V (D) −N) there exists an xN -arc in D). A digraph D is said to be kernel-perfect whenever each one of its induced subdigraphs has a kernel. A digraph D is oriented by sinks when every semicomplete subdigraph of ...

The lower boundW (K2n) ≥ 3n−2 is proved for the greatest possible number of colors in an interval edge coloring of the complete graph K2n. Let G = (V (G), E(G)) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G) is denoted by dG(x), the maximum degree of a vertex of G-by ∆(G), and the...

A G-protein binds to a G-protein-coupled-receptor (GPCR) by physical interactions between the amino acid sequences. Various physical properties of possible binding regions at the Cand N-termini of the α subunits of G-proteins were analyzed in order to classify the four families of α subunits; α s, α i/o, α q/11 and α 12/13, as well as the eight subfamilies. The distribution of the charge densit...

Let G be a profinite group and let α be an automorphism of G. Then α is topologically intense if, for every closed subgroup H of G, there exists x ∈ G such that α(H) = xHx. Topologically intense automorphisms are automatically continuous, because they stabilize each open normal subgroup of the group on which they are defined. We denote by Intc(G) the group of topologically intense automorphisms...

The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n2 and α ′ = a, or (2) a < n2 and there is a vertex v ∈ V (G) such that α(G − v) = a(G), where α is the critical independence number of the graph....

The stability number α(G) of the graph G is the size of a maximum stable set of G. If sk denotes the number of stable sets of cardinality k in graph G, then I(G;x) = s0 + s1x + ... + sαx α is the independence polynomial of G [12], where α = α(G) is the size of a maximum stable set. In this paper we prove that I(G;−1) satisfies |I(G;−1)| ≤ 2, where ν(G) equals the cyclomatic number of G, and the...

We prove that if G = (VG, EG) is a finite, simple, and undirected graph with κ components and independence number α(G), then there exist a positive integer k ∈ N and a function f : VG → N0 with non-negative integer values such that f(u) ≤ dG(u) for u ∈ VG, α(G) ≥ k ≥ ∑ u∈VG 1 dG(u)+1−f(u) , and ∑ u∈VG f(u) ≥ 2(k − κ). This result is a best-possible improvement of a result due to Harant and Schi...

Cladonia foliacea (CF) is a type of lichen belonging to the Cladoniaceae family, used as traditional medicine for various diseases. It known that CF has strong antioxidant and antidiabetic effects originating from secondary components. However, bioactivity significantly affected by extraction conditions such temperature, liquid/solid ratio, solvent type/concentration. Herein, parameters (temper...

The Lescure–Meyniel conjecture is the analogue of Hadwiger’s for immersion order. It states that every graph G contains complete Kχ(G) as an immersion, and like its minor-order counterpart it open even graphs with independence number 2. We show α(G)≥2 no hole length between 4 2α(G) satisfies this conjecture. In particular, C4-free α(G)=2 give another generalisation corollary, follows. Let H be ...