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.     

Spreads in Strongly Regular Graphs

A spread of a strongly regular graph is a partitionof the vertex set into cliques that meet Delsarte's bound (alsocalled Hoffman's bound). Such spreads give rise to coloringsmeeting Hoffman's lower bound for the chromatic number and tocertain imprimitive three-class association schemes. These correspondenceslead to conditions for existence. Most examples come from spreadsand fans in (partial) geometries. We give other examples, includinga spread in the McLaughlin graph. For strongly regular graphsrelated to regular two-graphs, spreads give lower bounds forthe number of non-isomorphic strongly regular graphs in the switchingclass of the regular two-graph.     

On 3-chromatic distance-regular graphs

We give some necessary conditions for a graph to be 3-chromatic in terms of the spectrum of the adjacency matrix. For all known distance-regular graphs it is determined whether they are 3-chromatic. A start is made with the classification of 3-chromatic distance-regular graphs, and it is shown that such graphs, if not complete 3-partite, must have λ ≤ 1.     

Comparison of different extraction methods for simultaneous determination of B complex vitamins in nutritional yeast using LC/MS-TOF and stable isotope dilution assay

The application of LC/MS-TOF method combined with stable isotope dilution assay was studied for determination of thiamine, riboflavin, nicotinamide, nicotinic acid, pantothenic acid, pyridoxal, and pyridoxine in food. Nutritional yeast powder was used as a model food matrix. Acid extraction was compared with various enzymatic treatments in ammonium formate buffer to find a suitable method for the conversion of more complex vitamers into the same forms as the used isotope-labeled internal standards. The enzyme preparations α-amylase, takadiastase, β-glucosidase, and acid phosphatase were all able to liberate thiamine and riboflavin. The diastatic enzyme preparations α-amylase and takadiastase also expressed proteolytic side activities resulting in the formation of small peptides which interfered with the mass spectra of thiamine and riboflavin. Liberation of nicotinamide and pantothenic acid from NAD⁺ and CoA, respectively, could not be achieved with any of the studied enzyme preparations. Hydrochloric acid extraction at 121 °C for 30 min was found to be destructive to pantothenic acid, but increased the liberation of pyridoxal.

Characterizing distance-regularity of graphs by the spectrum

We characterize the distance-regular Ivanov-Ivanov-Faradjev graph from the spectrum, and construct cospectral graphs of the Johnson graphs, Doubled Odd graphs, Grassmann graphs, Doubled Grassmann graphs, antipodal covers of complete bipartite graphs, and many of the Taylor graphs. We survey the known results on cospectral graphs of the Hamming graphs, and of all distance-regular graphs on at most 70 vertices.     

Changes in the secondary structure of proteins labeled with <Superscript>125</Superscript>I: CD spectroscopy and enzymatic activity studies

Summary Bovine serum albumin (BSA) and lysozyme (LSZ) were radiolabeled with ¹²⁵I. Three different methods for protein iodination with ¹²⁵I were optimized. Parameters like incubation time and ratio of oxidizing agent and amount of protein were established. During protein iodination with ¹²⁵I, structural damages caused by the introduction of iodine into the protein may occur. These damages depend on the oxidizing agent used and may lead to considerable changes in the protein structure and, hence, their biological activity. Changes in secondary structure of LSZ and BSA were examined by circular dichroism (CD). Enzymatic activity tests were performed with lysozyme to check its biological activity. The Iodo Bead was found the best oxidizing agent for protein iodination.     

Notes on simplicial rook graphs

The simplicial rook graph \(\mathrm{SR}(m,n)\) is the graph of which the vertices are the sequences of nonnegative integers of length m summing to n, where two such sequences are adjacent when they differ in precisely two places. We show that \(\mathrm{SR}(m,n)\) has integral eigenvalues, and smallest eigenvalue \(s = \max \left( -n, -{m \atopwithdelims ()2}\right) \), and that this graph has a large part of its spectrum in common with the Johnson graph \(J(m+n-1,n)\). We determine the automorphism group and several other properties.     

The graphs with all but two eigenvalues equal to $$$$ or 0

We determine all graphs for which the adjacency matrix has at most two eigenvalues (multiplicities included) not equal to \(-2\), or 0, and determine which of these graphs are determined by their adjacency spectrum.     

Cospectral graphs and the generalized adjacency matrix

Let J be the all-ones matrix, and let A denote the adjacency matrix of a graph. An old result of Johnson and Newman states that if two graphs are cospectral with respect to yJ − A for two distinct values of y, then they are cospectral for all y. Here we will focus on graphs cospectral with respect to yJ − A for exactly one value of y. We call such graphs -cospectral. It follows that is a rational number, and we prove existence of a pair of -cospectral graphs for every rational . In addition, we generate by computer all -cospectral pairs on at most nine vertices. Recently, Chesnokov and the second author constructed pairs of -cospectral graphs for all rational , where one graph is regular and the other one is not. This phenomenon is only possible for the mentioned values of , and by computer we find all such pairs of -cospectral graphs on at most eleven vertices.     

Universal adjacency matrices with two eigenvalues

Consider a graph Γ on n vertices with adjacency matrix A and degree sequence (d₁,…,d_n). A universal adjacency matrix of Γ is any matrix in Span {A,D,I,J} with a nonzero coefficient for A, where and I and J are the n×n identity and all-ones matrix, respectively. Thus a universal adjacency matrix is a common generalization of the adjacency, the Laplacian, the signless Laplacian and the Seidel matrix. We investigate graphs for which some universal adjacency matrix has just two eigenvalues. The regular ones are strongly regular, complete or empty, but several other interesting classes occur.