The Automorphism Groups of the Involution G-Graph and Cayley Graph *

International audienceLet G be a finite group and Φ(G, S) is the G−graph of a group G with respect to a non-empty subset S. The aim of this paper is to study the structure and the automorphism group of a simple form of G−graph for some finite groups like alternating group, dihedral, semi-dihedral, dicyclic, Zm δ Z2n, where δ is inverse mapping and V8n = {a, b|a 2n = b 4 = 1, aba = b −1 , ab −1 a = b}. Then we compare it with the automorphism group of the corresponding Cayley graph. Also we study the structure of involution G−graphs when S = Inv is the set of all involutions of G

Ihara Coefficients: A Flexible Tool for Higher Order Learning

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we propose a novel hypergraph characterization method by using the Ihara coefficients, i.e. the characteristic polynomial coefficients extracted from the Ihara zeta function. We investigate the flexibility of the Ihara coefficients for learning relational structures with different relational orders. Furthermore, we introduce an efficient method for computing the coefficients. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity in the hypergraph Laplacian. In experiments we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian. © 2010 Springer-Verlag Berlin Heidelberg

On constructing expander families of G-graphs

Like Cayley graphs, G-graphs are graphs that are constructed from groups. A method for constructing expander families of G-graphs is presented and is used to construct new expander families of irregular graphs. This technique depends on a relation between some known expander families of Cayley graphs and certain expander families of G-graphs. Several other properties of expander families of G-graphs are presented

Incidence graphs of bipartite G-graphs

Defining graphs from groups is a widely studied area motivated, for example, by communication networks. The most popular graphs defined by a group are Cayley graphs. G-graphs correspond to an alternative construction. After recalling the main properties of these graphs and their motivation, we propose a characterization result.With the help of this result, we show that the incidence graph of a symmetric bipartite G-graph is also a G-graph and we give a proof that, with some constraints, if the incidence graph of a symmetric bipartite graph is G-graph, the graph is also a G-graph. Using these results, we give an alternative proof for the fact that mesh of d-ary trees are G-graphs

Donor and recipient postoperative complications in living related kidney transplantation. A multicentric study

Background. Living related kidney transplantation is considered a gold standard of renal transplantation in order to overcome end-stage renal disease within the same family members. Living donation, albeit decreasing cadaveric donor shortage, exposes donors to the risk of surgical complications. Methods. In order to assess the postoperative complication rate in donors and recipients, we reviewed retrospectively 90 consecutive living related kidney transplants in a multicentric study. All nephrectomies were performed extraperitoneally through a left flank incision. Results. Major perioperative complications (first 3 weeks after surgery) occurred in 12 subjects: these included bleeding (2.2%), symptomatic pneumothorax (1.1%), iliac thrombophlebitis (3.3%), iliac artery dissection (1.1%), laparotomic dehiscence (2.2%), perirenal hematoma (1.1%), renal artery stenosis (1.1%), urinary fistula (1.1%). Minor perioperative complications took place in 8 cases. One recipient died. Donor postoperative major complications occurred in 2 subjects. Conclusions. On the basis of these results we conclude that living related kidney transplantation is an important treatment of end stage renal disease, due to the associated low major complication rate and the high feasibility of this methodology