Abstract
This article studies the notions of minimal and 1-redundant bearing rigidity. A necessary and sufficient condition for the numbers of edges in a graph of $n\,(n \geq 3)$ vertices to be minimally bearing rigid (MBR) in $\mathbb {R}^d\,(d \geq 2)$ is proposed. If $3 \leq n \leq d+1$ , a graph is MBR if and only if it is the cycle graph. In case $n > d+1$ , a generically bearing rigid graph is minimal if it has precisely $1 + \lfloor \frac{n-2}{d-1}\rfloor \times d + \text{mod}(n-2, d-1) + \text{sgn}(\text{mod}(n-2, d-1))$ edges. Then, several conditions for 1-redundant bearing rigidity are derived. Based on the mathematical conditions, some algorithms for generating generically, minimally, and 1-redundantly bearing rigid graphs are given. Furthermore, two applications of the new notions to optimal network design and formation merging are also reported.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
