The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...

A recently developed technique for the determination of the density of partition function zeroes using data coming from finite-size systems is extended to deal with cases where the zeroes are not restricted to a curve in the complex plane and/or come in degenerate sets. The efficacy of the approach is demonstrated by application to a number of models for which these features are manifest and th...

conclusions based on 8.2 mm cut-off point could differentiate 83% periapical granulomas and 79% radicular cysts from radiography images. background the distinction between radicular cysts and apical granulomas is important in treatment decision. objectives the current study aimed to differentiate these two lesions based on radiography images. results average size of radiography in periapical gr...