Nirmala energy

A novel vertex-degree-based topological invariant, called Nirmala index, was recently put forward, defined as the sum of the terms √ d ( u ) + d ( v ) over all edges u v of the underlying graph, where d ( u ) is the degree of the vertex u . Based on this index, we now introduce the respective “Nirmala matrix”, and consider its spectrum and energy. An interesting finding is that some spectral properties of the Nirmala matrix, including its energy, are related to the first Zagreb index.