Fixed Theorems in New Extended B Metric Spaces and Applications to System of Linear Equations

Abstract

The partition energy Pk(G) is defined as the sum
 of absolute values of k-partition eigenvalues of G. In this
 paper, we consider two regular graphs G and H with n and
 m vertices respectively and construct lexicographic product
 G[H] and G[H1], where H1 = H∇K1. We investigate the
 spectra and hence energy with respect to a partition Pn
 of these graphs and their generalized complements, which
 relate to the 1-partition energies of the factor graphs H
 providing a deeper understanding of their combined spectral
 characteristics. Further more, we construct graphs which are
 equienergetic with respect to partition Pn.