AUTHOR=Bilal Ahmad , Munir Muhammad Mobeen , Qureshi Muhammad Imran , Athar Muhammad 

TITLE=ISI spectral radii and ISI energies of graph operations

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1149006

DOI=10.3389/fphy.2023.1149006

ISSN=2296-424X

ABSTRACT=<p>Graph energy is defined to be the <italic>p</italic>-norm of adjacency matrix associated to the graph for <italic>p</italic> = 1 elaborated as the sum of the absolute eigenvalues of adjacency matrix. The graph’s spectral radius represents the adjacency matrix’s largest absolute eigenvalue. Applications for graph energies and spectral radii can be found in both molecular computing and computer science. On similar lines, Inverse Sum Indeg, (<italic>ISI</italic>) energies, and (<italic>ISI</italic>) spectral radii can be constructed. This article’s main focus is the <italic>ISI</italic> energies, and <italic>ISI</italic> spectral radii of the generalized splitting and shadow graphs constructed on any regular graph. These graphs can be representation of many physical models like networks, molecules and macromolecules, chains or channels. We actually compute the relations about the <italic>ISI</italic> energies and <italic>ISI</italic> spectral radii of the newly created graphs to those of the original graph.</p>