Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction cubic graphs. In this paper, we proved 3-edge-colorable 10-flow. This together with 4-color theorem implies bridgeless planar As byproduct, also show hamiltonian 8-flow.

Frustration index is a key measure for analysing signed networks that has been underused due to its computational complexity. We use an optimisation-based method to analyse frustration as a global structural property of signed networks under different contexts. We provide exact numerical results on social and biological signed networks as well as networks of formal alliances and antagonisms bet...

In a signed graph G, a negative clique is a complete subgraph having negative edges only. In this article, we give characteristic polynomial expressions, and eigenvalues of some signed graphs having negative cliques. This includes signed cycle graph, signed path graph, a complete graph with disjoint negative cliques, and star block graph with negative cliques.