Introduction: Carney COMPLEX is an autosomal dominant syndrome that is defined with different tumors including myxoma in different organs, endocrine tumors and lentiginosis lesions. This is the first case report of this syndrome from Iran.Case: The patient is a 27 year old girl, referred with flank pain. Physical examination revealed hirsutism, truncal obesity, hyperpigmantasion and hypertension; Cushing's syndrome was suggested and confirmed with related classic biochemical tests. She had history of cardiac myxoma during her childhood and had been operated twice.Pituitary microadenoma and right adrenal adenoma were reported on MRI and CT-scan, respectively. Initially laparascopic right adrenalectomy was done; as expected, no remission in signs of Cushing's syndrome was observed after surgery. By laparoscopic adrenalectomy of the other site, Cushing's syndrome resolved. Pathologic report of 1st operation was adrenal adenoma with surrounding pigmented micronodular hyperplasia and of the 2nd one was just pigmented micronodular hyperplasia.Conclusion: We have reported a patient with Carney syndrome along with Cushing's syndrome due to bilateral adrenal hyperplasia and an adenoma in contralateral adrenal and microadenoma of the pituitary as an incidentaloma. This is a new presentation of Carney syndrome.

We consider a class of hypergraphs called hypercycles and we show that a hypercycle Cnd,a is SHELLABLE or sequentially the Cohen-Macaulay if and only if nÎ{3,5}. Also, we characterize Cohen-Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.

Let G be a simple undirected graph and let Delta(G) be a simplicial COMPLEX whose faces correspond to the independent sets of G. A graph G is called SHELLABLE if Delta(G) is a SHELLABLE simplicial COMPLEX. We prove that the complement of a d-tree is a pure SHELLABLE graph. This generalizes a recent result of Ferrarello who used a theorem due to R. Froberg to prove that the complement of a d-tree is a Cohen-Macaulay graph. 

Introduction: Let G be a simple undirected graph over the vertex set V. Let I(G) denotes the edge ideal of G and DG be the simplicial COMPLEX whose faces correspond to the independent sets of G. This simplicial COMPLEX reflects many nice properties of G. A simplicial COMPLEX D is called SHELLABLE if the facets can given a linear order F1,…,Ft such that for all 1£t<f£s, there exists some vÎF1\Ft and some LÎ{1,…,f-1} with F1\Ft={v}. A result due to Hochster says that every pure SHELLABLE COMPLEX is Cohen-Macaulay over every field. A graph is called SHELLABLE, if the simplicial COMPLEX DG is a SHELLABLE simplicial COMPLEX.Aim: In this paper we focus on the question of what graphs G have the property that `G is Cohen-Macaulay, i.e. R/I(`G) is Cohen-Macaulay. We prove that the complement of a connected triangle-free graph is pure SHELLABLE and consequently Cohen-Macaulay.Methods: By providing an explicit shelling for the facets of D`G, whenever G is a connected triangle-free graph, we show `G, the complement of G, is pure SHELLABLE and consequently Cohen-Macaulay.Conclusion: The complement of any connected bipartite graph and any cycle is pure SHELLABLE and hence Cohen-Macaulay.

We give upper bounds for the regularity of edge ideal of some classes of graphs in terms of invariants of graph. We introduce two numbers a’ (G) and n (G) depending on graph G and show that for a vertex decomposable graphG, reg (R/I (G)) £ min{a’ (G), n (G)} and for a SHELLABLE graph G, reg (R/I (G))£n (G). Moreover, it is shown that for a graphG, where Gc is a d-tree, we have pd (R/I (G)) =maxvÎV (G) {degG (v)}.