The maximum order of adjacency matrices of graphs with a given rank

We look for the maximum order m(r) of the adjacency matrix A of a graph G with a fixed rank r, provided A has no repeated rows or all-zero row. Akbari, Cameron and Khosrovshahi conjecture that m(r)?=?2^(r+2)/2 ? 2 if r is even, and m(r)?=?5 · 2^(r?3)/2 ? 2 if r is odd. We prove the conjecture and characterize G in the case that G contains an induced subgraph ${\frac{r}{2}K_2}$ or ${\frac{r-3}{2}K_2+K_3}$ .     

Binary Codes of Strongly Regular Graphs

For strongly regular graphs ith adjacency matrix A, we look at the binary codes generated by A and A + I. We determine these codes for some families of graphs, e pay attention to the relation beteen the codes of switching equivalent graphs and, ith the exception of two parameter sets, we generate by computer the codes of all knon strongly regular graphs on fewer than 45 vertices.     

The chemical properties of 1-substituted 4-oxopyrimidinium cations

Some theoretical aspects of electrophilic properties of 4-pyrimidinium cations are discussed. The reactivity towards a series of C-, H-, N- and O-nucleophiles is studied.     

Tetrakis­[1‐(3‐chloro­propyl)‐1,2,4‐tri­azole‐κN4]­bis­(tetrafluoroborato‐κF)copper(II)

In the title complex, [Cu(BF₄)₂(1tpc)₄] [1tpc is 1‐(3‐chloro­propyl)‐1,2,4‐triazole, C₅H₈ClN₃], the copper(II) centres reside in a tetragonally distorted octahedral coordination environment. Four 1tpc ligands are coordinated to the metal atom via the N4 atom of the triazole rings in a square‐planar arrangement, with Cu—N bond lengths in the range 2.002 (2)–2.019 (2) Å. Two tetra­fluoro­borate anions, in the axial positions above and below the square plane, are weakly coordinated to the copper(II) centre, with Cu—F distances of 2.4009 (18) and 2.5096 (18) Å.     

Polymer-assisted solution-phase parallel synthesis of dipeptide p-nitroanilides and dipeptide diphenyl phosphonates

This letter describes the parallel synthesis of dipeptide p-nitroanilides (1) and dipeptide diphenyl phosphonates (2), compounds that can be used as substrates and irreversible inhibitors for the rapid profiling of dipeptidyl peptidases. A polymer-assisted solution-phase synthesis was used for a rapid and clean coupling between easily available building blocks.     

A revision of the alcoholysis and alkanethiolysis of 3‐amino‐6‐chloropyridazine

The synthesis of 3‐amino‐6‐alkoxy‐ and 3‐amino‐6‐alkylthiopyridazines via nucleophilic aromatic substitution on 3‐amino‐6‐chloropyridazine is described. In contrast to literature reports, no pressure tube is required to perform these reactions.     

The Life and Work of Joseph Plateau: Father of Film and Discoverer of Surface Tension

In 1835 Joseph Plateau (1801?C1883) was appointed Professor of Physics and Applied Physics at Ghent University, Belgium. By then he was well known for his groundbreaking work on the aftereffect of light on the human retina, and he would go on to become the first person to produce moving images, for which he is considered to be the Father of Film. His greatest scientific achievement, however, was his discovery of surface tension.     

A Characterization of Distance-Regular Graphs with Diameter Three

We characterize the distance-regular graphs with diameter three by giving an expression for the number of vertices at distance two from each given vertex, in terms of the spectrum of the graph.