A vertex set S is called a power dominating of graph G if every within the system monitored by following collection rules for grid monitoring. The domination number order minimal G. In this paper, we solve splitting and degree graph.

The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. This graph parameter was introduced by Chartrand et al. in 2008. The problem has garnered considerable interest and several variants of the initial version have since been intr...

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as supervised vertex regression task, where GNN trained predict current and injections at each grid branch that yield flow balance. By representing line graph with branches vertices, we can train accurate robust changes topology. In addition, by using spec...

A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs explain necessary sufficient conditions for construction cordial.

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (Note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely cartesian p...