The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. The sum of the absolute values of the real part of the eigenvalues is called the energy of the digraph. The extremal energy of bicyclic digraphs with vertex-disjoint directed cycles is known. In this paper, we consider a class of bicyclic digraphs with exactly two linear subdigraphs of equal length. We find the minimal an...

THE concept of HNN-extensions of groups was introduced by Higman, Neumann and Neumann in 1949. HNN-extensions and amalgamated free products have played a crucial role in combinatorial group theory, especially for algorithmic problems. In inverse semigroup theory there are many ways of constructing HNNextension in order to ensure the embeddability of the original inverse semigroup in the new one...

Intramolecular dipolar cycloaddition of bicyclic münchnones, 5H,7H-thiazolo[3,4-c]oxazol-4-ium-1-olates, derived from cyclodehydration of 2-substituted-N-acylthiazolidine-4-carboxylic acids are reported. A range of new pyrrolo[1,2-c]thiazole derivatives (7, 14, 15, 20, 23, and 26) were obtained as single enantiomers from 2-phenylthiazolidines, 2-benzoylthiazolidines, and 2-methylthiazolidine-4-...

A comprehensive product study, performed via the turbulent flow chemical ionization mass spectrometry (TF-CIMS) technique, of the primary OH-initiated oxidation of many of the atmospherically abundant aromatic compounds was performed. The bicyclic peroxy radical intermediate, a key proposed intermediate species in the Master Chemical Mechanism (MCM) for the atmospheric oxidation of aromatics, w...

This contribution describes the synthesis of several novel bicyclic α-amino endoperoxides, including CF(3)-substituted compounds, prepared by the aerobic electrochemical oxidation of a family of bicyclic aminocyclopropanes. These, in turn, are readily synthesised by a titanium-mediated intramolecular cyclopropanation process (Kulinkovich-de Meijere reaction), starting from N-alkenyl amides that...

We recently described a remarkable acid-catalyzed isomerization of bicyclic alkenes Ia and Ib to the betweenanenes IIa and IIb. ’ This finding suggested that certain larger ring betweenanenes might possess unusual stability relative to double bond isomers and might thus be derivable from readily available bicyclic compounds via equilibrating processes. In this report we describe several attempt...

Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n+, n−, n0) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n0 denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n− 2ν(G). Gu...

Condensed-bicyclic triazolo-thiadiazoles were synthesized via an efficient "green" catalyst strategy and identified as effective inhibitors of PTP1B in vitro. The lead compound, 6-(2-benzylphenyl)-3-phenyl-[1,2,4]triazolo[3][1,3,4]thiadiazole (BPTT) was most effective against human hepatoma cells, inhibits cell invasion, and decreases neovasculature in HUVEC and also tumor volume in EAT mouse m...

Compact codes, recently introduced (ref. 1), have been applied to all known bicyclic saturated hydrocarbons as the first step in a systematic deriving compact codes for more complex ring systems. The codes are compared with IUPAC nomenclature for bicyclic compounds, as well as with WLN (Wiswesser Line Notation). Advantages of the compact codes are outlined, including qualified algebraic manipul...

Cyclohexane analogues of the antifungal icofungipen [(1R,2S)-2-amino-4-methylenecyclopentanecarboxylic acid] were selectively synthesized from unsaturated bicyclic β-lactams by transformation of the ring olefinic bond through three different regio- and stereocontrolled hydroxylation techniques, followed by hydroxy group oxidation and oxo-methylene interconversion with a phosphorane. Starting fr...