In this paper, we shall prove that if the domination number of G is at most 2, then P (G,λ) is zero-free in the interval (1, β), where β = 2 + 1 6 3 √ 12 √ 93− 108− 1 6 3 √ 12 √ 93 + 108 = 1.317672196 · · · , and P (G, β) = 0 for some graph G with domination number 2. We also show that if ∆(G) ≥ v(G) − 2, then P (G,λ) is zero-free in the interval (1, β′), where β′ = 5 3 + 1 6 3 √ 12 √ 69− 44− 1...

A β-perfect graph is a simple graph G such that χ(G′) = β(G′) for every induced subgraph G′ of G, where χ(G′) is the chromatic number of G′, and β(G′) is defined as the maximum over all induced subgraphs H of G′ of the minimum vertex degree in H plus 1 (i.e., δ(H) + 1). The vertices of a β-perfect graph G can be coloured with χ(G) colours in polynomial time (greedily). The main purpose of this ...

For α≥1, β≥0, and a graph G, spanning subgraph H of G is said to be an (α,β)-spanner if dist(u,v,H)≤α⋅dist(u,v,G)+β holds for any pair vertices u v. These type spanners, called linear generalizes additive spanners multiplicative spanners. Recently, Fomin, Golovach, Lochet, Misra, Saurabh, Sharma initiated the study directed graphs (IPEC 2020). In this article, we continue line research prove th...

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ⊆ E(G) such that G \ X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded? ...

Let G = (V, E) be a simple graph with vertex set V and edge set E. Let D be a subset of V, and let B(D) be the set of neighbours of D in V \ D. The differential ∂(D) of D is defined as |B(D)| − |D|. The maximum value of ∂(D) taken over all subsets D ⊆ V is the differential ∂(G) of G. For β ∈ (−1, ∆), the β-differential ∂β(G) of G is the maximum value of {|B(D)| − β|D| : D ⊆ V}. Motivated by an ...

In cat atrial myocytes, β-adrenergic receptor (β-AR) stimulation exerts profound effects on excitation-contraction coupling and cellular Ca(2+) cycling that are mediated by β(1)- and β(2)-AR subtypes coupled to G proteins (G(s) and G(i)). In this study, we determined the effects of β-AR stimulation on pacing-induced Ca(2+) alternans. Ca(2+) alternans was recorded from single cat atrial myocytes...

An innovative one-step synthesis towards β-aryl-β,β-difluorocarbamates and β-aryl-β,β-difluoroazides is presented. The described approach relies on the use of α-fluorostyrene substrates in a radical addition/fluorination reaction with N-centered radicals presence Selectfluor®. best results were obtained for azidofluorination reaction. resultant further transformed into Nitrogen-based heterocycl...