Hypomorphy of graphs up to complementation

Let $V$ be a set of cardinality $v$ (possibly infinite). Two graphs $G$ and $G'$ with vertex set $V$ are {\it isomorphic up to complementation} if $G'$ is isomorphic to $G$ or to the complement $\bar G$ of $G$. Let $k$ be a non-negative integer, $G$ and $G'$ are {\it $k$-hypomorphic up to complementation} if for every $k$-element subset $K$ of $V$, the induced subgraphs $G\_{\restriction K}$ and $G'\_{\restriction K}$ are isomorphic up to complementation. A graph $G$ is {\it $k$-reconstructible up to complementation} if every graph $G'$ which is $k$-hypomorphic to $G$ up to complementation is in fact isomorphic to $G$ up to complementation. We give a partial characterisation of the set $\mathcal S$ of pairs $(n,k)$ such that two graphs $G$ and $G'$ on the same set of $n$ vertices are equal up to complementation whenever they are $k$-hypomorphic up to complementation. We prove in particular that $\mathcal S$ contains all pairs $(n,k)$ such that $4\leq k\leq n-4$. We also prove that 4 is the least integer $k$ such that every graph $G$ having a large number $n$ of vertices is $k$-reconstructible up to complementation; this answers a question raised by P. Ill

Fatigue Behavior of Short Glass Fiber Reinforced Polyamide 66: Experimental Study and Fatigue Damage Modelling

The aim of the present paper is to study and model the fatigue behavior of short glass fibers reinforced polyamide-66. The effect of fiber content on the fatigue and static behavior of this composite is investigated. In such composites fatigue damage growth exhibits three stages. A continuum damage based model is presented to predict damage evolution during these three stages. Experimental results show that increasing the fiber content increases the elastic modulus and the tensile strength of the studied materials under tensile tests. However, the rupture behavior changes from ductile to brittle. Moreover increasing the fiber percentage changes the S-N curves slope and decreases the fatigue life. Analytical results predicted by the proposed model, compared to experimental ones shows good agreement and the developed model predicted fatigue damage growth in its three stages of evolution with good performance

EFFICIENT NUMERICAL MODELLING OF FUNCTIONALLY GRADED SHELL MECHANICAL BEHAVIOR

Numerical analysis of the static bending and free vibration mechanical behavior of FGM are performed using the UMAT-USDFLD subroutines in ABAQUS software. Different combinations of geometries, mechanical loading and boundary conditions are adopted. The material properties according to the coordinates of the integration points are defined in the developed numerical model. The First Order Deformation Theory is used for thin and moderately thick FG shells analysis. The accuracy and the robustness of the numerical model are illustrated through the solution of several non trivial structure problems. The proposed numerical procedure is significantly efficient from the computational point of view

(-1)-Hypomorphic Graphs with the Same 3-Element Homogeneous Subsets

International audienc