The Isomorphism Problem of Power Graphs and a Question of Cameron

The isomorphism problem for graphs (GI) and the isomorphism problem for groups (GrISO) have been studied extensively by researchers. The current best algorithms for both these problems run in quasipolynomial time. In this paper, we study the isomorphism problem of graphs that are defined in terms of groups, namely power graphs, directed power graphs, and enhanced power graphs. It is not enough to check the isomorphism of the underlying groups to solve the isomorphism problem of such graphs as the power graphs (or the directed power graphs or the enhanced power graphs) of two nonisomorphic groups can be isomorphic. Nevertheless, it is interesting to ask if the underlying group structure can be exploited to design better isomorphism algorithms for these graphs. We design polynomial time algorithms for the isomorphism problems for the power graphs, the directed power graphs and the enhanced power graphs arising from finite nilpotent groups. In contrast, no polynomial time algorithm is known for the group isomorphism problem, even for nilpotent groups of class 2. We note that our algorithm does not require the underlying groups of the input graphs to be given. The isomorphism problems of power graphs and enhanced power graphs are solved by first computing the directed power graphs from the input graphs. The problem of efficiently computing the directed power graph from the power graph or the enhanced power graph is due to Cameron [IJGT'22]. Therefore, we give a solution to Cameron's question.Comment: 23 page

ASSESSMENT OF PATIENTS’ KNOWLEDGE, ATTITUDE AND PRACTICE REGARDING DIABETES MELLITUS IN A TERTIARY CARE HOSPITAL IN EASTERN INDIA

Objectives: Proper assessment and understanding of knowledge, attitude and practice among diabetic population towards this disease is important as diabetes needs lifelong adoption of healthy lifestyles for prevention and control. This study aimed to assess diabetic patients’ knowledge, attitude and practice regarding diabetes mellitus in a tertiary care hospital. Methods: This cross sectional, observational and questionnaire based study was conducted over a period of two months on diabetic patients attending diabetic clinic. A pretested structured questionnaire consisting of 24 items was administered through face-to-face interview. Results: Responses from 129 subjects were analyzed. Most of the subjects could not define diabetes (60.45%), identified the symptoms of diabetes (polyurea 62.79% and polyphagia 55.81%), and knew that lifestyle modification was necessary to control diabetes (exercise 66.66%, dietary modification 62.79%). However they had notion that bitter substances could cure diabetes (51.93%) and insulin should be avoided (28.68%). Majority of the subjects did not monitor blood glucose at home (81.4%) and did not take care of their feet (59.69%). Patients’ knowledge was positively associated with family history, duration of diabetes and level of education. Duration of diabetes and educational level were positively associated with practice of the patients.   Conclusion: Present study reflects that diabetic patients require support and guidance for practicing better disease management. Role of a clinical pharmacist and clinical activities like patient counselling and pharmaceutical care program may help in improving patients’ knowledge, attitude and practice for managing diabetes

FACTORS ASSOCIATED WITH LOW BIRTH WEIGHT BABY: A CROSS-SECTIONAL STUDY IN A TERTIARY CARE HOSPITAL

Objectives: Low birth weight is a challenging multifaceted public health problem due to its association with increased risk of morbidity and mortality of infants. Both community and institution based studies are needed to find out the lacunae regarding occurrence of low birth weight babies, so that effective strategies which are relevant to the local conditions can be adopted for its prevention. We conducted this study to estimate the prevalence and determine the factors associated with low birth weight in the live born infants delivered in a tertiary care hospital. Methods: This was an observational, cross-sectional questionnaire-based study done in the Department of Pharmacology and Department of Gynaecology and Obstetrics in this tertiary care hospital. Mothers who gave birth to their baby in the Obstetrics Ward were included. The subjects underwent a face-to-face interview using a suitably designed and validated questionnaire and the data were collected. Results: A total of 360 subjects were interviewed. 34.7% of mothers were below 20 yrs of age. Majority of the mother had education up to secondary level (58.33%) and were housewife (82.22%). 58.2% of mothers belonged to family size of 5-10 members. Among the 104 low birth weight infants, 63.46% were small for date and 36.54% were preterm. The mean weight of the newborn was 2.54 kg. Maternal age, number of family members, number of anti natal care visits, anemia maternal weight gain during pregnancy were associated with low birth weight (p<0.05). No significant differences were found among the newborns with and without low birth weight regarding the variables like religion, family type, maternal addiction, pervious abortion and tetanus toxoid taken by the mother. Conclusion: As low birth weight is the major cause of perinatal morbidity and mortality, every step should be taken for its prevention. In this regard, proper maternal education for antenatal care and regular visit to antenatal care clinic should be done. Field workers may help to impart correct knowledge of diet through proper health education besides providing other advices like delaying the age of first child, birth spacing, and family planning services utilization.     &nbsp