Open AccessNirmala energy
Author(s) -
Ivan Gutman,
Veerabhadrappa R. Kulli
Publication year - 2021
Publication title -
open journal of discrete applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2617-9687
pISSN - 2617-9679
DOI - 10.30538/psrp-odam2021.0055
Subject(s) - vertex (graph theory) , combinatorics , invariant (physics) , mathematics , degree (music) , matrix (chemical analysis) , graph , spectral graph theory , discrete mathematics , physics , mathematical physics , line graph , graph power , materials science , composite material , acoustics
A novel vertex-degree-based topological invariant, called Nirmala index, was recently put forward, defined as the sum of the terms \(\sqrt{d(u)+d(v)}\) over all edges \(uv\) 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.