Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146

Trees whose 2-domination subdivision number is 2

A set $S$ of vertices in a graph $G = (V,E)$ is a $2$-dominating set if every vertex of $V\setminus S$ is adjacent to at least two vertices of $S$. The $2$-domination number of a graph $G$, denoted by $\gamma_2(G)$, is the minimum size of a $2$-dominating set of $G$. The $2$-domination subdivision number $sd_{\gamma_2}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the $2$-domination number. The authors have recently proved that for any tree $T$ of order at least $3$, $1 \leq sd_{\gamma_2}(T)\leq 2$. In this paper we provide a constructive characterization of the trees whose $2$-domination subdivision number is $2$

Bounds on several versions of restrained domination number

We investigate several versions of restraineddomination numbers and present new bounds on these parameters. We generalize theconcept of restrained domination and improve some well-known bounds in the literature.In particular, for a graph $G$ of order $n$ and minimum degree $\delta\geq 3$, we prove thatthe restrained double domination number of $G$ is at most $n-\delta+1$. In addition,for a connected cubic graph $G$ of order $n$ we show thatthe total restrained domination number of $G$ is at least $n/3$ andthe restrained double domination number of $G$ is at least $n/2$