Factor-Critical Property in 3-Dominating-Critical Graphs

A vertex subset $S$ of a graph $G$ is a dominating set if every vertex of $G$ either belongs to $S$ or is adjacent to a vertex of $S$. The cardinality of a smallest dominating set is called the dominating number of $G$ and is denoted by $\gamma(G)$. A graph $G$ is said to be $\gamma$- vertex-critical if $\gamma(G-v)< \gamma(G)$, for every vertex $v$ in $G$. Let $G$ be a 2-connected $K_{1,5}$-free 3-vertex-critical graph. For any vertex $v \in V(G)$, we show that $G-v$ has a perfect matching (except two graphs), which is a conjecture posed by Ananchuen and Plummer.Comment: 8 page

Progress of simulations for reacting shear layers

An attempt was made to develop a high speed, chemically reactive shear layer test rig. The purpose of the experiment was to study the mixing of oxidizer and fuel streams in reacting shear layers for various density, velocity, and Mach number. The primary goal was to understand the effects of the compressibility upon mixing and combustion in a fundamental way. Therefore, a two-dimensional shear layer is highly desirable for its simplicity to quantify the compressibility effects. The RPLUS 2D code is used to calculate the flow fields of different sections of the test rig. The emphasis was on the supersonic nozzle design, the vitiation process for the hot air stream and the overall thermodynamic conditions of the test matrix. The k-epsilon turbulence model with wall function was successfully implemented in the RPLUS code. The k and epsilon equations are solved simultaneously and the LU scheme is used to make it compatible with the flow solver