Degree Sums and Covering Cycles

It is shown that if in a simple graph G of order n the sum of degrees of any three pairwise non-adjacent vertices is at least n, then there are two cycles (or one cycle and an edge or a vertex) of GF that contain all the vertices. © 1995 John Wiley & Sons, Inc.     

Prediction of structural and thermodynamic properties of three products: 1-bromobenzene, tetrachlorethylene and 4-hydroxy-chromen-2-one using numerical methods

Our work concerns interaction spherical study of three toxic products, bromobenzene, tetrachloroethylene, and 4-hydroxy-chromene-2-one; using the Leap Frog algorithm, we calculated new values of cut-off of the box through Lennard-Jones potential parameters. This model was adapted to allow the determination of the characteristics for the SP₁, SP₂ and SP₃ state points and was applied to study the properties for the three products by molecular dynamics. This method provides an advantage to confirm the structure–activity relationship for these compounds. We calculated the thermodynamic and structural properties for both canonical NVT and isothermal–isobaric NPT ensembles of these products. Numerical system results have been compared with both experimental data and recent investigation theoretical. Our simulation model isobaric–isothermal system gives accurate results, and comparing with the canonical system, this model agrees very well with the experimental data. We aim to demonstrate that the classical approach with a low statistical uncertainty for liquid toxic leads to data in very good agreement with experiment or other types of calculations. We obtained a good prediction of the thermodynamic properties. We hope that this model with a lower threshold to 2.5σ could be an effective starting material for studying the properties of complex systems.     

Robust fuzzy fault detection and isolation approach applied to surge in centrifugal compressor modeling and control

This work presents the results of applying an advanced fault detection and isolation technique to centrifugal compressor; this advanced technique uses physics models of the centrifugal compressor with a fuzzy modeling and control solution method. The fuzzy fault detection and isolation has become an issue of primary importance in modern process engineering automation as it provides the prerequisites for the task of fault detection. In this work, we present an application of this approach in fault detection and isolation of surge in compression system. The ability to detect the surge is essential to improve reliability and security of the gas compressor plants. We describe and illustrate an alternative implementation to the compression systems supervision task using the basic principles of fuzzy fault detection and isolation associated with fuzzy modeling approach. In this supervision task, the residual generation is obtained from the real input-output data process and the residual evaluation is based on fuzzy logic method. The results of this application are very encouraging with relatively low levels of false alarms and obtaining a good limitation of surge in natural gas pipeline compressors.     

Regular path decompositions of odd regular graphs

Kotzig asked in 1979 what are necessary and sufficient conditions for a d‐regular simple graph to admit a decomposition into paths of length d for odd d>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable to a decomposition of the graph into paths of length 3 where the middle edges of the paths coincide with the 1‐factor. We conjecture that existence of a 1‐factor is indeed a sufficient condition for Kotzig's problem. For general odd regular graphs, most 1‐factors appear to be extendable and we show that for the family of simple 5‐regular graphs with no cycles of length 4, all 1‐factors are extendable. However, for d>3 we found infinite families of d‐regular simple graphs with non‐extendable 1‐factors. Few authors have studied the decompositions of general regular graphs. We present examples and open problems; in particular, we conjecture that in planar 5‐regular graphs all 1‐factors are extendable. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 114–128, 2010     

Sufficient Condition for the Existence of an Even [a, b]-Factor in Graph

Let a, b, be two even integers. In this paper, we get a sufficient condition which involves the stability number, the minimum degree of the graph for the existence of an even [a, b]-factor.     

Neighborhoods and Covering Vertices by Cycles

G =(V,E) is a 2-connected graph, and X is a set of vertices of G such that for every pair x,x' in X, , and the minimum degree of the induced graph <X> is at least 3, then X is covered by one cycle. This result will be in fact generalised by considering tuples instead of pairs of vertices. Let be the minimum degree in the induced graph <X>. For any , . If , and , then X is covered by at most (p-1) cycles of G. If furthermore , (p-1) cycles are sufficient. So we deduce the following: Let p and t () be two integers. Let G be a 2-connected graph of order n, of minimum degree at least t. If , and , then V is covered by at most cycles, where k is the connectivity of G. If furthermore , (p-1) cycles are sufficient. In particular, if and , then G is hamiltonian. Received April 3, 1998     

Stability number and [a,b]‐factors in graphs

A spanning subgraph whose vertices have degrees belonging to the interval [a,b], where a and b are positive integers, such that a ≤ b, is called an [a,b]‐factor. In this paper, we prove sufficient conditions for existence of an [a,b]‐factor, a connected [a,b]‐factor, and a 2‐connected [a,b]‐factor. The conditions involve the minimum degree, the stability number, and the connectivity of a graph. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 254–264, 2004     

Bounds for the b-chromatic number of some families of graphs

In this paper we obtain some upper bounds for the b-chromatic number of K_1,s-free graphs, graphs with given minimum clique partition and bipartite graphs. These bounds are given in terms of either the clique number or the chromatic number of a graph or the biclique number for a bipartite graph. We show that all the bounds are tight.