The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...

We report new measurements of the branching fraction B(Ds+→ℓ+ν), where ℓ+ is either μ+ or τ+(→π+ν¯τ), based on 6.32 fb−1 electron-positron annihilation data collected by BESIII experiment at six center-of-mass energy points between 4.178 and 4.226 GeV. Simultaneously floating Ds+→μ+νμ Ds+→τ+ντ components yields B(Ds+→τ+ντ)=(5.21±0.25±0.17)×10−2, B(Ds+→μ+νμ)=(5.35±0.13±0.16)×10−3, ratio decay wi...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

With the newly available data sets on hadronic τ decays from theB-factories BABAR and BELLE, and future data from BESIII, precise information on the decay distributions will soon become available. This calls for an improvement of the decay spectra also on the theoretical side. In this work, the distribution function for the decay τ → ντKπ will be presented with the relevantKπ vector and scalar ...