
For natural numbers
In this paper, we introduce the zero-divisor graph
A unit distance graph is a finite simple graph which may be drawn on the plane so that its vertices are represented by distinct points and the edges are represented by closed line segments of unit length. In this paper, we show that the only primitive strongly regular unit distance graphs are
Pooling designs are standard experimental tools in many biotechnical applications. In this paper, we construct a family of error-correcting pooling designs with the incidence matrix of two types of subspaces of singular symplectic spaces over finite fields.
In
In order to characterize convex polyhedra with regular polygonal faces by a minimal number of parameters, we first introduce some new parameters, then we analyze a table of their values to see how well different sets of parameters tell these solids apart, and finally we present their characterization by four parameters.
In this paper, we show a short proof of the
A non-empty
Let
In this paper, we constructed two multireceiver authentication codes from singular symplectic geometry over finite fields. Under the assumption that the probability distribution on the source states and sender’s key space is uniform, the parameters and success probabilities of different types of deceptions are also computed.
An oriented coloring of a directed graph is a vertex coloring in which no two adjacent vertices belong to the same color class and all of the arcs between any two color classes have the same direction. Injective oriented colorings are oriented colorings that satisfy the extra condition that no two in-neighbors of a vertex receive the same color. The oriented chromatic number of an unoriented graph is the maximum oriented chromatic number over all possible orientations. Similarly, the injective oriented chromatic number of an unoriented graph is the maximum injective oriented chromatic number over all possible orientations. The main results obtained in this paper are bounds on the injective oriented chromatic number of two-dimensional grid graphs.
Let
The values of the Ramsey numbers
In this paper, we correct three other errata of [3], proving that
We use dynamic programming to compute the domination number of the Cartesian product of two directed paths,
In 1975, Erdős proposed the problem of determining the maximal number of edges in a graph on
This paper develops the polyhedral approach to integer partitions. We consider the set of partitions of an integer
Like the Coxeter graph becoming reattached into the Klein graph in [3], the Levi graphs of the
Let
In this paper, we study a pair of simplicial complexes, which we denote by
Let
In this paper, some formulae for computing the numbers of spanning trees of the corona and the join of graphs are deduced.
Partially filled
Stankova and West proved in 2002 that the patterns
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