Neighbors degree sum energy of graphs

Abstract

In this paper, we introduce a new matrix for a graph G in which i th row sum and i th column sum are both equal to neighbors degree sum of i th vertex and define a new variant of graph energy called neighbors degree sum energy $$E_{N} (G)$$ of a graph G. The striking feature of this new matrix is that it is related with some well known degree based topological indices like Zagreb type indices, forgotten indices, etc. When $$E_N(G)$$ values of some molecules containing hetero atoms are correlated with their total $$\pi $$ –electron energy, we got a good correlation with the correlation coefficient $$r=0.982$$ . $$E_N(G)$$ values of some selected 25 polyaromatic hydrocarbons also showed excellent correlation with their $$\pi $$ –electron energy values with the correlation coefficient $$r=0.997$$ . Further, we computed neighbors degree sum energy of some standard classes of graphs and established some bounds and characterizations on largest eigenvalue of N(G) and neighbors degree sum energy of graphs.