Roman domination is an historically inspired variety of domination in graphs, in which
vertices are assigned a value from the set $\{0, 1, 2\} $ in such a way that every vertex …

Let γ i (Cm⎕ Cn) denote the independent domination number of the strong product of the
graphs Cm, the cycle of length m, m≥ 3 and the graph Cn, the cycle of length n, n≥ 3. In this …

Using algebraic approach we implement a constant time algorithm for computing the
domination numbers of the Cartesian products of paths and cycles. Closed formulas are …

The Hamiltonian path problem for general grid graphs is known to be NP‐complete. In this
paper, we give necessary and sufficient conditions for the existence of Hamiltonian paths in …

The longest path problem is the problem of finding a simple path with the maximum number
of vertices in a given graph, and so far it has been solved polynomially only for a few classes …

A dominator coloring of a graph G is a proper coloring of G with the additional property that
every vertex dominates an entire color class. The dominator chromatic number χ _d (G) χ d …

In this paper, we have considered the coverage problem in wireless sensor network (WSN)
on a convex subset of R^2. Sensors are dropped from the air randomly on some pre-fixed …

Coverage in wireless sensor networks (WSNs) is a well-studied problem. In most of the
situation WSNs have two-dimensional bounded continuous domain. In practice, sensors …

Let G=(V, E) be a simple graph. A subset D⊆ V is a dominating set if every vertex not in D is
adjacent to a vertex in D. The domination number of G, denoted by γ (G), is the smallest …

Bulog is a state-owned public company engaged in food logistics. There are about 18 Bulog
warehouses in East Java Province with an uneven distribution. Because the scope of …