covering arrays of strength two have been widely studied as combinatorial models of software interaction test suites for pairwise testing. while numerous algorithmic techniques have been developed for the generation of covering arrays with few columns (factors), the construction of covering arrays with many factors and few tests by these techniques is problematic. random generation techniques c...

in this note first by considering the notion of general fuzzy automata (for simplicity gfa), we define the notions of direct product, restricted direct product and join of two gfa. also, we introduce some operations on (fuzzy) sets and then prove some related theorems. finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given gfa....

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number γP (G) of G is the minimum cardinality of a power dominating set. Dorfling and Henning [2] determined the power domination number of the Cartesian product of paths. I...

The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

Abstract—In graph theory, different types of products of two graphs had been studied, e.g., Cartesian product, Tensor product, Strong product, etc. In this paper we generalize the concept of Cartesian product of graphs.We define 2 Cartesian product and more generally r Cartesian product of two graphs. We study these product mainly for path graphs. We also discuss connectedness of the new graph.