In this paper we show that the connectivity of the kth power of a graph of connectivity m is at least km if the kth power of the graph is not a complete graph. Also, we. prove th at removing as many as k 2 vertices from the kth power of a graph (k ;;. 3) leaves a Hamiltonian graph, and that removing as many as k 3 vertices from the kth power of a graph (k;;' 3) leaves a Hamiltonian con nected g...

Power flow analyses are essential for the correct operation of power grids, however, electricity systems becoming increasingly complex to analyze with conventional numerical methods. The present work proposes a typed graph neural network based approach solve problem. networks trained on benchmark grid cases which modified by varying injections (load and generation), branch characteristics topol...