let $r$ be a commutative ring and $m$ be an $r$-module with $t(m)$ as subset,   the set of torsion elements. the total graph of the module denoted   by $t(gamma(m))$, is the (undirected) graph with all elements of   $m$ as vertices, and for distinct elements  $n,m in m$, the   vertices $n$ and $m$ are adjacent if and only if $n+m in t(m)$. in this paper we   study the domination number of $t(ga...

It has been shown that one triangulation of a set of points can be converted to any other triangulation of the same set of points by a sequence of edge flip operations. In this paper we consider a tesselation of a set of points consisting of convex cells, a convex subdivision, and explore the notion of flipping edges from one convex subdivision of the points to another, where both subdivisions ...

We propose an adaptive geometry compression method based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. In the meantime, we provide high-s...

A set D of vertices of a graph G is a dominating set if every vertex in V \D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set of G. The domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the domination number. Arumugam h...

Given a graph G = (V, E), the subdivision of an edge e = uv ∈ E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G...

The rainbow game domination subdivision number of a graph G is defined by the following game. Two players D and A, D playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided. The game ends when all the edges of G are marked or subdivided and results in a new graph G′. The purpose of D is to minimize the 2-rainbow dominating number γr2(G ′) of G′ while A t...

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...