Let τ(G) and bind(G) be the toughness and binding number, respectively, of a graph G. Woodall observed in 1973 that τ(G) > bind(G) − 1. In this paper we obtain best possible improvements of this inequality except when (1+ √ 5)/2 < bind(G) < 2 and bind(G) has even denominator when expressed in lowest terms.

Conceptually graph vulnerability relates to the study of graphintactness when some of its elements are removed. The motivation forstudying vulnerability measures is derived from design and analysisof networks under hostile environment. Graph tenacity has been anactive area of research since the the concept was introduced in1992. The tenacity T(G) of a graph G is defined asbegin{center} $T(G)=di...

If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.In this paper we discuss...

following our previous presentation of a new three-fold symmetry for derivation of the magic numbers of nuclei based upon a quark state model of nuclei, here the nuclear binding energy is obtained from such new perspective. from this point of view, since each nucleon is made of three quarks, the binding energy of nuclei contains a volume term proportional to 3a (a is mass number). by considerin...

apotransferrin (apo tf)  in 0.1 m n-(2hydroxyethyl)piperazine-n2-ethanesulfanic acid at 25 ˚c  and ph 7.4 has been titrated with acidic solution of tb3+. the binding of tb3+ at  the two specific metal-binding sites of transferrin was followed from the changes in the difference uv spectra at 245 nm. the molar absorptivity per binding site for tb3+-tf is 22,500 ± 1000 m-1cm-1. to determine the tb...