Graphs of Maximal Energy with Fixed Maximal Degree

TL;DR

This paper establishes bounds on the energy of graphs with a fixed maximum degree using elementary methods, extending previous results for regular graphs to more general cases.

Contribution

It provides a new, elementary proof for bounds on graph energy based on second and fourth moments, generalizing prior regular graph results.

Findings

Derived bounds for graph energy in terms of moments

Extended regular graph energy bounds to non-regular graphs

Used elementary methods for proofs

Abstract

We give a bound for the graph energy with given maximal degree in terms of the second and fourth moments of a graph. In the case in which the graph is $d$-regular we obtain the bound that is given in Van Dam, E. et al. (2014). through elementary methods.