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

Revision of Failed Radial Head Arthroplasty.

BACKGROUND: Revision of radial head arthroplasty (RHA) may be indicated in cases of prosthesis loosening and malposition. Inherent difficulties in revision surgery include poor bone stock and disrupted soft tissue envelope. Although cases of RHA used for revision of failed RHA are rare, there is reasonable expectation for increasing frequency of these cases due to the increasing incidence of primary RHA. Furthermore, there is an increasing demand for postoperative recovery of function; thus, surgeons may consider revising a failed RHA to a new RHA. We report on series of failed RHA which were revised to a new radial head prosthesis. METHODS: A retrospective review was performed at multiple institutions for a single radial head prosthesis used for revision of a failed radial head prosthesis. Clinical and radiographic outcomes were collected with a minimum of 1 year of follow-up. RESULTS: Across 11 patients at a mean follow-up of 45.1 months, the mean Mayo Elbow Performance Score was 81.7; mean Disabilities of the Arm, Shoulder, and Hand scores were 24.4; and mean Visual Analog Scale for pain was 0.6. Radiographic analysis yielded no evidence of capitellar wear or stem loosening. CONCLUSION: A radial head prosthesis can produce satisfactory results when used for revision of a failed prosthesis. Inherent difficulties in revision surgery include the potential for reduced bone stock and a disrupted soft tissue envelope. Elements of prosthesis design which may contribute to effectively managing revision surgery include a long stem with in-growth surface and prosthetic head alignment to the axis of forearm rotation