European Journal of Combinatorics Index, Volume 27

BACKGROUND: Diabetes is an inflammatory condition associated with iron abnormalities and increased oxidative damage. We aimed to investigate how diabetes affects the interrelationships between these pathogenic mechanisms. METHODS: Glycaemic control, serum iron, proteins involved in iron homeostasis, global antioxidant capacity and levels of antioxidants and peroxidation products were measured in 39 type 1 and 67 type 2 diabetic patients and 100 control subjects. RESULTS: Although serum iron was lower in diabetes, serum ferritin was elevated in type 2 diabetes (p = 0.02). This increase was not related to inflammation (C-reactive protein) but inversely correlated with soluble transferrin receptors (r = - 0.38, p = 0.002). Haptoglobin was higher in both type 1 and type 2 diabetes (p &lt; 0.001) and haemopexin was higher in type 2 diabetes (p &lt; 0.001). The relation between C-reactive protein and haemopexin was lost in type 2 diabetes (r = 0.15, p = 0.27 vs r = 0.63, p &lt; 0.001 in type 1 diabetes and r = 0.36, p = 0.001 in controls). Haemopexin levels were independently determined by triacylglycerol (R(2) = 0.43) and the diabetic state (R(2) = 0.13). Regarding oxidative stress status, lower antioxidant concentrations were found for retinol and uric acid in type 1 diabetes, alpha-tocopherol and ascorbate in type 2 diabetes and protein thiols in both types. These decreases were partially explained by metabolic-, inflammatory- and iron alterations. An additional independent effect of the diabetic state on the oxidative stress status could be identified (R(2) = 0.5-0.14). CONCLUSIONS: Circulating proteins, body iron stores, inflammation, oxidative stress and their interrelationships are abnormal in patients with diabetes and differ between type 1 and type 2 diabetes</p

On the split structure of lifted groups

Let ▫$wp colon tilde{X} to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$rm{CT}_wp$▫ being abelian. Assuming that a group of automorphisms ▫$G le rm{Aut} X$▫ lifts along $wp$ to a group ▫$tilde{G} le rm{Aut} tilde{X}$▫, the problem whether the corresponding exact sequence ▫$rm{id} to rm{CT}_wp to tilde{G} to G to rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$tilde{G}$▫ nor the action ▫$Gto rm{Aut} rm{CT}_wp$▫ nor a 2-cocycle ▫$G times G to rm{CT}_wp$▫, are given. Explicitly constructing the cover ▫$tilde{X}$▫ together with ▫$rm{CT}_wp$▫ and ▫$tilde{G}$▫ as permutation groups on ▫$tilde{X}$▫ is time and space consuming whenever ▫$rm{CT}_wp$▫ is largethus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group)one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$rm{CT}_wp$▫ is elementary abelian.Naj bo ▫$wp colon tilde{X} to X$▫ regularna krovna projekcija povezanih grafov, grupa krovnih transformacij ▫$rm{CT}_wp$▫ pa naj bo abelova. Ob predpostavki, da se grupa avtomorfizmov ▫$G le rm{Aut} X$▫ dvigne vzdolž ▫$wp$▫ do grupe ▫$tilde{G} le rm{Aut} tilde{X}$▫, podrobno analiziramo problem, ali se ustrezno eksaktno zaporedje ▫$rm{id} to rm{CT}_wp to tilde{G} to G to rm{id}$▫ razcepi glede na Cayleyevo dodelitev napetosti, ki rekonstruira projekcijo do ekvivalence natančno. V gornjem kombinatoričnem sestavu je razširitev podana samo implicitno: podani niso ne ▫$tilde{G}$▫ ne delovanje ▫$Gto rm{Aut} rm{CT}_wp$▫ ne 2-kocikel ▫$G times G to rm{CT}_wp$▫. Eksplicitno konstruiranje krova ▫$tilde{X}$▫ ter ▫$rm{CT}_wp$▫ in ▫$tilde{G}$▫ kot permutacijskih grup na ▫$tilde{X}$▫ je časovno in prostorsko zahtevno vselej, kadar je ▫$rm{CT}_wp$▫ veliktako je uporaba implementiranih algoritmov (na primer, HasComplement v Magmi) vse prej kot optimalna. Namesto tega pokažemo, da lahko najnujnejšo informacijo o delovanju in 2-kociklu učinkovito izluščimo neposredno iz napetosti (ne da bi eksplicitno konstruirali krov in dvignjeno grupo)zdaj bi bilo mogoče uporabiti standardno metodo reduciranja problema na reševanje sistema linearnih enačb nad celimi števili. Vendar tukaj uberemo malce drugačen pristop, ki sploh ne zahteva nobenega poznavanja kohomologije. Časovno in prostorsko zahtevnost formalno analiziramo za vse primere, ko je ▫$rm{CT}_wp$▫ elementarna abelova

Cubic symmetric graphs of order a small number times a prime or a prime square

AbstractA graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular elementary abelian coverings of the complete bipartite graph K3,3 and the s-regular cyclic or elementary abelian coverings of the complete graph K4 for each s⩾1 are classified when the fibre-preserving automorphism groups act arc-transitively. A new infinite family of cubic 1-regular graphs with girth 12 is found, in which the smallest one has order 2058. As an interesting application, a complete list of pairwise non-isomorphic s-regular cubic graphs of order 4p, 6p, 4p2 or 6p2 is given for each s⩾1 and each prime p

Invariant subspaces, duality, and covers of the Petersen graph

AbstractA general method for finding elementary abelian regular covering projections of finite connected graphs is applied to the Petersen graph. As a result, a complete list of pairwise non-isomorphic elementary abelian covers admitting a lift of a vertex-transitive group of automorphisms is given. The resulting graphs are explicitly described in terms of voltage assignments