A set S of vertices of a graph G = (V ,E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number γt (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) i...

An edge-magic total labeling of a graph G is a one-toone map λ from V (G) ∪ E(G) onto the integers {1, 2, · · · , |V (G) ∪ E(G)|} with the property that, there is an integer constant c such that λ(x) + λ(x, y) + λ(y) = c for any (x, y) ∈ E(G). If λ(V (G)) = {1, 2, · · · , |V (G|} then edge-magic total labeling is called super edgemagic total labeling. In this paper we formulate super edge-magic...

In this paper, the exponential stabilization of chained form system with inertia is addressed. A discontinuous static time invariant control law is proposed that achieves exponential stability in the Lyapunov’s sense. Such a result was previously obtained only by means of time varying feedback or hybrid feedback endowed of memory capabilities. The total number of switching is less or equal to t...

In this paper, we compute topological indices of the total graphs of the tadpole graphs, wheel graphs and ladder graphs using the subdivision concept, which extend the results of Ranjini et al. (2011).

An acyclic coloring of a graph G is an assignment of colors to the vertices of G such that no two adjacent vertices receive the same color and every cycle in G has vertices of at least three different colors. An acyclic k-coloring of G is an acyclic coloring of G with at most k colors. It is NP-complete to decide whether a planar graph G with maximum degree four admits an acyclic 3-coloring [1]...

The recent non-uniform subdivision approach extends traditional uniform subdivision schemes with variable rules, offering additional shape parameters (such as knot spacings) for feature control. Despite its flexibility, shape modification based on non-uniform subdivision usually requires designers to interactively adjust a large number of degrees of freedom (DOFs) to achieve the desired shapes,...

Subdivision surfaces are a powerful model widely used in geometric modelling. Controlling the accuracy of the approximation of the limit surface often involves the computation of the distance between the control mesh and the limit surface. Nevertheless, the a priori level (or depth) of subdivision based on a distance criterion has not yet been expressed. The goal of this paper is thus to comput...

A Roman dominating function on a graph G = (V,E) is a function f : V −→ {0, 1, 2} satisfying the condition that every vertex v for which f(v) = 0 is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function is the value w(f) = ∑ v∈V f(v). The Roman domination number of a graph G, denoted by γR(G), equals the minimum weight of a Roman dominating function on ...