Cherlin, Harrington and Lachlan’s paper on ω0-categorical, ω0-stable theories ([CHL]) was the starting point of geometrical stability theory. The progress made since then allows us better to understand what they did in modern terms (see [PI]) and also to push the description of totally categorical theories further, (see [HR1, AZ1, AZ2]). The first two sections of what follows give an exposition...

In this paper, we study the level lowering problem for mod 2 representations of the absolute Galois group of a totally real field F. In the case F = Q, this was done by Buzzard; here, we generalise some of Buzzard’s results to higher weight and arbitrary totally real fields, using Rajaei’s generalisation of Ribet’s theorem and previous work of Fujiwara and the author. 2000 Mathematics Subject C...

A graph G is said to have totally magic cordial(TMC) labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0)− nf (1)| ≤ 1, where nf (i)(i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we investigate some new families of graphs that admit totally magic cordial labeli...

Article history: Received 23 August 2012 Available online xxxx Communicated by Luchezar L. Avramov MSC: 16G50 13B02 16E65

In a network, each arc is assigned a weight. The weight of a path or a cycle is defined as the minimum weight of its arcs. The maximum of weights of all paths between two nodes is defined as the strength of connectedness between the nodes. In network applications, the reduction in the strength of connectedness is more relevant than the total disconnection of the graph. A graph is totally weight...