The Zagreb indices of graphs with a given clique number

AbstractFor a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let Wn,k be the set of connected n-vertex graphs with clique number k. In this work we characterize the graphs from Wn,k with extremal (maximal and minimal) Zagreb indices, and determine the values of corresponding indices

Tension band wiring for simple olecranon fractures: evaluation of surgical technique

Abstract Background In some settings, specific techniques for open reduction and internal fixation are preferred based on the eminence of a surgeon or professional organization. An emphasis on technical aspects of surgery that are not proved superior and vary substantially from surgeon to surgeon can be confusing for trainees. This study applied a numerical grading of the technical aspects of tension band wire (TBW) fixation for olecranon fracture; assessed the interobserver agreement of each criterion; and measured the correlation of the technical grading and objective and subjective long-term outcomes. Materials and methods Forty observers were invited to rate the technical aspects of TBW fixation of the olecranon on 26 post-operative radiographs. The interobserver reliability of the rating was measured using the intra-class correlation coefficient. The correlation between the rating and motion, Mayo elbow performance index, and disabilities of the arm, shoulder and hand score was tested with the Spearman’s rank correlation test. Results None of the figure-of-eight TBW constructs were considered perfect according to the numerical grading: the majority of observers found three deviations per fixation. The interobserver agreement was only fair for the total number of deviations and no correlation between the number of deviations and long-term objective and subjective outcome was found. Conclusions A rating of the technical aspects of TBW for olecranon fractures was unreliable and did not correlate with subjective and objective outcomes. Emphasis on specific technical aspects of fixation might be confusing for trainees and could distract them from the principles of effective treatment. Level of evidence Level IV diagnostic study

Radiographic assessment of calcifying tendinitis of the rotator cuff : an inter- and intraobserver study

The radiographic appearance of calcific tendinitis of the rotator cuff varies according to the stage of the disease. We compared currently used classification systems in a large group of observers to identify the most reliable classification system. Thirty-seven orthopaedic surgeons evaluated shoulder radiographs of 25 patients to classify the stage of the calcific tendinitis according to the classifications by (1) Gärtner and (2) Molé on a Web-based study platform. Inter and intraobserver agreement among observers was measured using the Siegel and Castellan multirater κ. Both classification systems had fair interobserver agreement : κ was 0.25 for the Molé classification and 0.34 for the Gärtner classification. The Gärtner classification was significantly more reliable than the Molé classification. Currently there is no radiographic classification that can serve the purpose of guiding the treatment in a reliable way