Two new tetracyclic triterpenoid trilocularol A and trilocularol A 3-glucoside and one pentacyclic triterpenoid tirlocularoside A were isolated from Corchorus trilocularis L., their structure were elucidated as 3beta,6alpha,16alpha,20(S),27-pentahydroxydammar-24(Z)-ene (1), 3beta-D-glucopyranosyloxy-6alpha,16alpha,20(S),27-tetrahydroxydammar-24(Z)-ene (2) and 2alpha,3beta,19alpha,30-tetrahydrox...

Pentacyclic analogues of the potent voltage-gated sodium ion channel agonist batrachotoxin can be accessed through an intermediate furan by exploiting Diels-Alder cycloaddition reactions with ring-strained dienophiles. The use of 3-bromofuran as a 1,2-dianion equivalent, the application of carbamate reductive N-alkylation for homomorpholine ring assembly, and the demonstration of CsF as an effe...

A series of pentacyclic heterocyclic systems (15 examples, 69-89%) have been synthesized using intramolecular Povarov reactions involving 3-aminocoumarins and O-cinnamylsalicylaldehydes. The Povarov adducts are formed with high selectivity for the trans,trans relative stereochemistry in the newly-formed [6,6] fused ring system. One example of a Povarov adduct featuring a new [6,5] fused ring sy...

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...

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...

Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

See examples in Fig. 1(b). Many graph algorithms use an st-orientation. For instance, graph drawing algorithms [3], [4], [17], [19], [22], routing algorithms [1], [13] and partitioning algorithms [14]. Given a biconnected graph G and its two vertices s and t, one can find an st-orientation of G in O(m + n) time [5], [6], [22]. Note that if G is not biconnected then G may have no st-orientation....

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. 2009 Wiley Periodicals, Inc. J Graph Theory 62: 369–384, 2009