the zagreb indices are the oldest graph invariants used in mathematical chemistry to predictthe chemical phenomena. in this paper we define the multiple versions of zagreb indicesbased on degrees of vertices in a given graph and then we compute the first and secondextremal graphs for them.

in this work, a bench-scale process was developed using mineral-processing methods to recover iron from a placer deposit located in bardaskan, khorasan-e-razavi, iran. the mineralogical studies were performed by x-ray diffraction (xrd), x-ray fluorescence (xrf), electron probe micro-analyzer (epma), and an optical microscope. these studies indicated that titanomagnetite, magnetite, and hematite...

the degree set of a graph is the set of its degrees. kapoor et al. [degree sets for graphs, fund. math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. furthermore, the minimum order of such a graph is determined. a graph is 2-self- centered if its radius and diameter are two. in this paper for ...

background: sleep apnea is associated with increased risk ofdiabetes mellitus. however, no studies have compared sleep apneasymptoms in diabetic patients and their first degree relatives.the purpose of our study was to investigate high risk for sleepapnea syndrome, in diabetics and their first degree relatives forprevention of diabetes in family.methods: as a part of a cohort study, all of diab...

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...

abstract in order to investigate the freezing tolerance of field grown fennel (fueniculum vulgare mill) under controlled conditions, a factorial experiment based on completely randomized design was conducted with three replications in agricultural college, ferdowsi university of mashhad in 2004. treatments were two fennel ecotypes (khorasan and kerman), two planting dates (oct 8th and 29th ) an...

the prime graph $gamma(g)$ of a group $g$ is a graph with vertex set $pi(g)$, the set of primes dividing the order of $g$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $g$ of order $pq$. let $pi(g)={p_{1},p_{2},...,p_{k}}$. for $pinpi(g)$, set $deg(p):=|{q inpi(g)| psim q}|$, which is called the degree of $p$. we also set $d(g):...

We introduce the notion of a degree spectrum of a complete theory to be the set of Turing degrees that contain a copy of some model of the theory. We generate examples showing that not all degree spectra of theories are degree spectra of structures and vice-versa. To this end, we give a new necessary condition on the degree spectrum of a structure, specifically showing that the set of PA degree...

let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

a recently published paper [t. došlić, this journal 3 (2012) 25-34] considers the zagrebindices of benzenoid systems, and points out their low discriminativity. we show thatanalogous results hold for a variety of vertex-degree-based molecular structure descriptorsthat are being studied in contemporary mathematical chemistry. we also show that theseresults are straightforwardly obtained by using...