‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n...

the first zagreb index, $m_1(g)$, and second zagreb index, $m_2(g)$, of the graph $g$ is defined as $m_{1}(g)=sum_{vin v(g)}d^{2}(v)$ and $m_{2}(g)=sum_{e=uvin e(g)}d(u)d(v),$ where $d(u)$ denotes the degree of vertex $u$. in this paper, the firstand second maximum values of the first and second zagreb indicesin the class of all $n-$vertex tetracyclic graphs are presented.

A connected graph with a cyclomatic number k is said to be k-cyclic graph. We obtain the formula for of labelled non-planar pentacyclic graphs given vertices, and find asymptotics planar tetracyclic n vertices as → ∞. prove that under uniform probability distribution on set consideration, asymptotically equal 1089/1105, labeled 1591/1675.

A new domino reaction for the highly selective synthesis of tetracyclic cinnolino[5,4,3-cde]cinnolines using steric control was described. In this reaction, the use of anthenes with aliphatic groups (R(1)) leads to cinnolino[5,4,3-cde]cinnolines whereas anthenes with aryl groups (R(1)) result in N-amino-1,8-dioxoacridines.

We report the hydrogen isotope ratio H/H (expressed as dH values) of 8 selected hopanes, tricyclic and tetracyclic terpanes from oils and source rocks in the Potiguar Basin, and of associated formation water. Hopanes ranged in dH value from !79‰ to !142‰, whereas triand tetracyclic terpanes (TTTs) ranged from !137‰ to !225‰. Formation water dH values ranged from !23‰ to !32‰. The most significa...

An enantioselective and diastereoselective approach toward the synthesis of the tetracyclic scaffold of the furanobutenolide-derived polycyclic norditerpenoids is described. Focusing on synthetic efforts toward ineleganolide, the synthetic approach utilizes a palladium-catalyzed enantioselective allylic alkylation for the construction of the requisite chiral tertiary ether. A diastereoselective...

A study of the chemical constituents from the Australian Sponge Hyrtios digitatus has provided a perspective on the connection between the chemistry and biology of the puupehenones, a unique and unusual class of merosesquiterpenes. In this study, a new tetracyclic merosesquiterpene, 19-methoxy-9,15-ene-puupehenol (1) was isolated from the marine sponge Hyrtios digitatus along with the known 20-...

Aiming at restricting the conformational freedom of tryptophan-containing peptide ligands, we designed a THBC (tetrahydro-β-carboline)-DKP (diketopiperazine)-based peptidomimetic scaffold capable of arranging in an unusual α-turn conformation. The synthesis is based on a diastereoselective Pictet-Spengler condensation to give the THBC core, followed by an intramolecular lactamization to complet...