The graph energy game

12/28/2020

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by   Gerardo Arizmendi, et al.

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We study the graph energy from a cooperative game viewpoint. We introduce the graph energy game and show various properties. In particular, we see that it is a superadditive game and that the energy of a vertex, as defined in Arizmendi and Juarez-Romero (2018), belongs to the core of the game. These properties imply new bounds for the energy of graphs. We also consider a version based on p-Schatten norms.