Minimum Cycle Base of Graphs Identified by Two Planar Graphs

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds

Shortest Co-cycle Bases of Graphs

In this paper we investigate the structure of the shortest co-cycle base(or SCB in short) of connected graphs, which are related with map geometries, i.e., Smarandache 2-dimensional manifolds. By using a Hall type theorem for base transformation, we show that the shortest co-cycle bases have the same structure (there is a 1-1 correspondence between two shortest co-cycle bases such that the corresponding elements have the same length). As an application in surface topology, we show that in an embedded graph on a surface any nonseparating cycle can’t be generated by separating cycles. Based on this result, we show that in a 2-connected graph embedded in a surface, there is a set of surface nonseparating cycles which can span the cycle space. In particular, there is a shortest base consisting surface nonseparating cycle and all such bases have the same structure. This extends a Tutte’s result

The 3-D vision system integrated dexterous hand

Most multifingered hands use a tendon mechanism to minimize the size and weight of the hand. Such tendon mechanisms suffer from the problems of striction and friction of the tendons resulting in a reduction of control accuracy. A design for a 3-D vision system integrated dexterous hand with motor control is described which overcomes these problems. The proposed hand is composed of three three-jointed grasping fingers with tactile sensors on their tips, a two-jointed eye finger with a cross-shaped laser beam emitting diode in its distal part. The two non-grasping fingers allow 3-D vision capability and can rotate around the hand to see and measure the sides of grasped objects and the task environment. An algorithm that determines the range and local orientation of the contact surface using a cross-shaped laser beam is introduced along with some potential applications. An efficient method for finger force calculation is presented which uses the measured contact surface normals of an object