• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.1069-1073
• /
• 1997

We characterize supersolvable signed graphs by using simplicial nodes and some signed graphs $\Delta_2, L_k$.

• Journal of Communications and Networks
• /
• v.16 no.6
• /
• pp.667-676
• /
• 2014

Connectivity is a crucial quality of service measure in wireless sensor networks. However, the network is always at risk of being split into several disconnected components owing to the sensor failures caused by various factors. To handle the connectivity problem, this paper introduces an in-advance mechanism to prevent network partitioning in the initial deployment phase. The approach is implemented in a distributed manner, and every node only needs to know local information of its 1-hop neighbors, which makes the approach scalable to large networks. The goal of the proposed mechanism is twofold. First, critical nodes are locally detected by the critical node detection (CND) algorithm based on the concept of maximal simplicial complex, and backups are arranged to tolerate their failures. Second, under a greedy rule, topological holes within the maximal simplicial complex as another potential risk to the network connectivity are patched step by step. Finally, we demonstrate the effectiveness of the proposed algorithm through simulation experiments.