The graph energy game

TL;DR

This paper introduces the graph energy game, analyzing its properties and deriving new bounds for graph energy using cooperative game theory, including a variant based on p-Schatten norms.

Contribution

It presents the novel concept of the graph energy game, proves its superadditivity, and connects vertex energy to the core, providing new bounds and a Schatten norm variant.

Findings

Graph energy game is superadditive.

Vertex energy belongs to the core of the game.

New bounds for graph energy are established.

Abstract

We study the graph energy from a cooperative game viewpoint. We introduce \emph{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.