Evolutionary Algorithms for Searching Almost-Equienergetic Graphs

Many real-world problems can be modeled using graphs. This representation allows us to understand some important aspects of problem behavior through the calculation of different measures. The energy of a graph is an invariant measure that has gained interest in network analysis due to its recent applications, then it is interesting to know the structural properties that make two graphs with similar energies.In this work we propose the search for almost-equienergetic graphs using evolutionary algorithms for Erdös-Rényi networks and trees. The proposed evolutionary algorithms are able to obtain almost-equienergetic graphs in larger instances with respect to traditional methods and the results lead to analyze interesting properties of the graphs found.