48 research outputs found
Integral group ring of the McLaughlin simple group
We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs
Some Structural Resuits on Prime Graphs
Given a graph G = (V,E), a subset M of V is a module [17] (or an interval [10] or an autonomous [11] or a clan [8] or a homogeneous set [7] ) of G provided that x ∼ M for each vertex x outside M. So V,φ and {x}, where x ∈ V , are modules of G, called trivial modules. The graph G is indecomposable [16] if all the modules of G are trivial. Otherwise we say that G is decomposable . The prime graph G is an indecomposable graph with at least four vertices. Let G and H be two graphs. Let If G has no induced subgraph isomorphic to H, then we say that G is H-free. In this paper, we will prove the next theore
Integral group ring of the McLaughlin simple group
We consider the Zassenhaus conjecture for the
normalized unit group of the integral group ring of the McLaughlin
sporadic group McL. As a consequence, we confirm for this group
the Kimmerle’s conjecture on prime graphs
NLC-2 graph recognition and isomorphism
NLC-width is a variant of clique-width with many application in graph
algorithmic. This paper is devoted to graphs of NLC-width two. After giving new
structural properties of the class, we propose a -time algorithm,
improving Johansson's algorithm \cite{Johansson00}. Moreover, our alogrithm is
simple to understand. The above properties and algorithm allow us to propose a
robust -time isomorphism algorithm for NLC-2 graphs. As far as we
know, it is the first polynomial-time algorithm.Comment: soumis \`{a} WG 2007; 12