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‎let $g=(v(g),e(g))$ be a graph‎, ‎$gamma_t(g)$. let $ooir(g)$ be the total domination and oo-irredundance number of $g$‎, ‎respectively‎. ‎a total dominating set $s$ of $g$ is called a $textit{total perfect code}$ if every vertex in $v(g)$ is adjacent to exactly one vertex of $s$‎. ‎in this paper‎, ‎we show that if $g$ has a total perfect code‎, ‎then $gamma_t(g)=ooir(g)$‎. ‎as a consequence, ...

The Hong Kong cadastral system is designed for efficient transactions which has remained unchanged since the enactment of the Land Registration Ordinance in 1844. In this British designed cadastral system, various land-right records are kept by different government departments. The current computerized register gives good protection of ownership rights to practically all land properties. Land u...

Subdivision rules create sequences of nested cell structures on CWcomplexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that a subdivision rule for a hyperbolic group determines the Gromov boundary. We give a criterion for a subdivisi...

In geometric models with high-valence vertices, current subdivision wavelets may not deal with the special cases well for good visual effect of multiresolution surfaces. In this paper, we present the novel biorthogonal polar subdivision wavelets, which can efficiently perform wavelet analysis to the control nets with polar structures. The polar subdivision can generate more natural subdivision ...

An eternal $m$-secure set of a graph $G = (V,E)$ is aset $S_0subseteq V$ that can defend against any sequence ofsingle-vertex attacks by means of multiple-guard shifts along theedges of $G$. A suitable placement of the guards is called aneternal $m$-secure set. The eternal $m$-security number$sigma_m(G)$ is the minimum cardinality among all eternal$m$-secure sets in $G$. An edge $uvin E(G)$ is ...

Under the premise that land administration is one of the necessary components of sustainable development and better land management, this article reviews how progressive titling could foster new land administration procedures and associated information systems. This review is based on the objectives of progressive titling as they are developed or currently implemented in various regions in the ...

Subdivision surface method is a series of iterative operation adopts a certain subdivision formula for an initial grid, obtains the smooth limits surface finally, and can dispose any arbitrary complex topology grid. At present most of the subdivision algorithm are 1-4 subdivisions and as the number of subdivision increase, the grid grow so toorapid in the number of patch that it is difficult fo...