The antiregular connected graph onrvertices is defined as the connected graph whose vertex degrees take the values ofr−1distinct positive integers. We explore the spectrum of its adjacency matrix and show common properties with those of connected threshold graphs, having an equitable partition with a minimal numberrof parts. Structural and combinatorial properties can be deduced for related classes of graphs and in particular for the minimal configurations in the class of singular graphs.

A young man was treated in hospital for sepsis, disseminated intravascular coagulation and multi-organ failure. He was a regular intranasal cocaine user up to 1 day prior to symptom onset. Clinical examination revealed extensive retiform purpura affecting both his lower limbs. Skin biopsy revealed widespread thrombosis in the small- and medium-sized vessels of the mid dermis and the subcutaneous fat with surrounding leucocytoclasis. There was also extensive ischaemic necrosis of the upper reticular and papillary dermis and focal ischaemic necrosis of the epidermis. These findings were in keeping with a thrombotic vasculopathy with associated cutaneous ischaemic necrosis, likely associated with levamisole-adulterated cocaine (LAC). An autoimmune screen showed extremely raised levels of anti-B2-glycoprotein IgM, IgG and anti-cardiolipin IgG antibodies, usually seen in antiphospholipid syndrome (APS). The literature describes how APS could be secondary to various underlying conditions, including LAC, and that levamisole toxicity may mimic APS and hence be missed.

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A 91-year-old Caucasian man on warfarin for atrial fibrillation presented in view of sudden-onset haemoptysis with fresh bleeding with clots immediately after having eaten a piping-hot traditional cheesecake (pastizz) and burning the soft-palate of his mouth. The haemoptysis had resolved by the time that the patient had arrived to hospital. On examination, a 2 cm by 2 cm dark red, solitary mass could be seen just anterior to the uvula. This was not causing any pain or discomfort to the patient. Blood results were mostly unremarkable except for a raised international normalised ratio (INR) of 3.53. The patient was administered 5 mg vitamin K orally in attempt to lower the INR level and warfarin was subsequently omitted for 7 days. He was also prescribed oral steroids on discharge. The lesion resolved in 7 days and warfarin was restarted then with no further consequences.

This is a retrospective study intended to determine the prevalence of severe hypoglycaemia requiring admission to Mater Dei Hospital from January to December 2018. We identified risk factors associated with hospital admission and conducted a survival analysis of the cohort.All patients admitted with diabetes and hypoglycaemia were identified by means of hospital admission database, clinical notes, discharge summaries and iSOFT clinical manager. A Cox regression model and a multivariate analysis were utilised to study survival analysis at one year after admission in relation to management strategies, comorbidity and length of hospital stay.A total of 167 episodes (0.77%) of hypoglycaemia admissions satisfying inclusion criteria were identified out of 21,589 medical admissions. Type 2 diabetes (T2DM) was present in 154 patients (92.2%), mean age was 71.5 years (SD 15.5) and mean length of stay was 4.4 days (SD 5.3). A survival analysis showed a negative association with a higher Charlson Comorbidity Index (CCI) score (95% CI 1.132-1.516, p<0.05), Parkinson's disease (95% CI 0.078-0.670, p<0.05) and residing in care homes (95% CI 0.274-0.982, p<0.05). Length of stay was related to a poor CCI score (95% CI 0.251-0.967), peripheral vascular disease (95% CI -4.658-0.764), and malignancy (95% CI -5.438-0.205). There seemed to be no correlation between different diabetes treatment regimens and length of hospital stay or survival.These findings show a strong link between hypoglycaemia, decreased survival and increased frailty in elderly patients with type 2 diabetes. This study highlights a need for better education and less stringent glycaemic targets for vulnerable patients.