if $g$ is a connected graph with vertex set $v$, then the eccentric connectivity index of $g$, $xi^c(g)$, is defined as $sum_{vin v(g)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. in this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

We introduce and study the notion of a logarithmic vertex algebra, which is algebra with singularities in operator product expansion quantum fields; thus providing rigorous formulation algebraic properties fields conformal field theory. develop framework that allows many results about algebras to be extended algebras, including particular Borcherds identity Kac Existence Theorem. Several exampl...

In this paper, the structure of cocommutative vertex bialgebras is investigated. For a general bialgebra V, it proved that set G(V) group-like elements naturally an abelian semigroup, whereas P(V) primitive Lie algebra. g∈G(V), denote by Vg connected component containing g. Among main results, if V bialgebra, then V=⊕g∈G(V)Vg, where V1 subbialgebra which isomorphic to VP(V) associated algebra P...

a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...

Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topologi...

objective(s): the development of reliable and ecofriendly process for the synthesis of nano-metals is an important aspect in the field of nanotechnology. nano-metals are a special group of materials with broad area of applications. materials and methods: in this study, extracellular synthesis of silver nanoparticles (snps) performed by use of the gram positive soil streptomycetes. streptomycete...

to enhance solubility and the performance of a plant gum (from south peach tree of china, sp gum) as a drilling fluid additive, we explored the potential of modified sp (msp) gum by modifying it with epichlorohydrin. the modification conditions, such as the mass ratio of  the crosslinking agent, ph and temperature, were optimized and the results show that 56.40 g/100g mass ratio of the crosslin...

introduction: clinical policies of “10 steps of breast feeding” proposed by world health organization (who) can promote breast feeding. the goal of this study was to evaluate breast feeding in the first hour after birth and its relation to the influencing factors. material and methods: in this cross-sectional study, the data is related to mothers and infants referring to two baby friendly hospi...