In this paper, we analyze ptolemaic graphs for its properties as chordal graphs. Firstly, two characterizations of ptolemaic graphs are proved. The first one is based on the reduced clique graph, a structure that was defined by Habib and Stacho [8]. In the second one, we simplify the characterization presented by Uehara and Uno [13] with a new proof. Then, known subclasses of ptolemaic graphs a...

Ptolemaic graphs are graphs that satisfy ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. The graph class can also be seen as a natural generalization of block graphs (and hence trees). In this paper, a new characterization of ptolemaic graphs is presented. It is a canonical tree representation based on...

Abstract. In this work we announce the Maple package conley to compute connection and C-connection matrices. conley is based on our abstract homological algebra package homalg. We emphasize that the notion of braids is irrelevant for the definition and for the computation of such matrices. We introduce the notion of triangles that suffices to state the definition of (C)-connection matrices. The...

Given a class of graphs, G, a graph G is a probe graph of G if its vertices can be partitioned into two sets, P (the probes) and N (the nonprobes), where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. In this paper we study the probe graphs of ptolemaic graphs when the partition of vertices is unknown. We present some characteri...

Barakat syndrome, also known as hypoparathyroidism, sensorineural deafness, and renal dysplasia syndrome is an extremely rare congenital disorder. Different etiologies are described for the syndrome but the definite pathophysiology remains unclear. Hereby, we present a case of Barakat syndrome who was diagnosed on the basis of clinical and molecular data.

quṭb al-dīn al-shīrāzī (634h/1236ce-710h/1311ce) wrote four major works on astronomy: nihāyat al‐idrāk fī dirāyat al‐aflāk (“the utmost attainment in comprehending the orbs), in arabic, first edition completed mid-shaʿbān 680/november 1281); the ikhtiyārāt‐i muẓaffarī (“selections for muẓaffar al-dīn arslan” [a minor ruler in qasṭamūnī (modern kastamonu, turkey)], in persian, completed sometime...

Ptolemaic graphs are those satisfying the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. It can also be seen as a natural generalization of block graphs (and hence trees). In this paper, we first state a laminar structure of cliques, which leads to its canonical tree representation. This result is a t...