Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

in this paper, a new online robot motion planner is developed for systematically exploring unknown environâ¬ments by intelligent mobile robots in real-time applications. the algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. it does so by online calculation of the generalized voronoi graph (gvg) of the free space, and utilizing a combination of depth-first an...

We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The example is based on the characterization of vertex-edge pseudo-visibility graphs of O’Rourke and Streinu [Proc. ACM Symp. Comput. Geometry, Nice, France, 1997, pp. 119–128] and extends a recent result of the author [Proc. ACM Symp. Comput. Geometry, Miami Be...

‎The Narumi-Katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎Let $G$ be a ‎simple graph with vertex set $V = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $G$‎. ‎The Narumi-Katayama ‎index is defined as $NK(G) = prod_{vin V}d(v)$‎. ‎In this paper,‎ ‎the Narumi-Katayama index is generalized using a $n$-ve...

To precisely reach for an object with a humanoid robot, it is of central importance to have good knowledge of both end-effector, object pose and shape. In this work we propose a framework for markerless visual servoing on unknown objects, which is divided in four main parts: I) a leastsquares minimization problem is formulated to find the volume of the object graspable by the robot’s hand using...

Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon C and a finite set P of points in general position in the complement of C, the visibility graph GC(P ) has a vertex for each point in P and an edge pq for any two points p and q in P that can see ...

Optimal point-to-point trajectory planning for planar redundant manipulator is considered in this study. The main objective is to minimize the sum of the position error of the end-effector at each intermediate point along the trajectory so that the end-effector can track the prescribed trajectory accurately. An algorithm combining Genetic Algorithm and Pattern Search as a Generalized Pattern Se...

In this paper we present an approach for a pursuit-evasion problem that considers a 2.5d environment represented by a height map. Such a representation is particularly suitable for large-scale outdoor pursuit-evasion. By allowing height information we not only capture some aspects of 3d visibility but can also consider target heights. In our approach we construct a graph representation of the e...

The Position and orientation accuracy of robot manipulator has long become a major issue to be considered in its advanced application. The simplified expressions for the differential vector of the end-effector have been proposed based on the original expressions derived by Veitschegger and Wu in 1986. According to this new expression, a linear error model that described the end-effector positio...