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.

在本文中，我们为图G引入了一个新矩阵，其中第i 行和第i列均等于第i个顶点的邻居度和，并定义了一种新的图能量变体，称为邻居度和能量\（图G的E_ {N}（G）\）。该新矩阵的显着特征是，它与一些众所周知的基于度的拓扑指数（例如Zagreb类型指数，遗忘指数等）相关。当某些包含杂原子的分子的\（E_N（G）\）值与其总\（\ pi \）–电子能量，我们与相关系数有很好的相关性 \（r = 0.982 \）。某些选定的25种多芳烃的\（E_N（G）\）值也与它们的\（\ pi \）–电子能量值具有极好的相关性，相关系数为\（r = 0.997 \）。此外，我们计算了一些标准类图的邻居度和能量，并建立了N（G）的最大特征值和图的邻居度和能量的界限和特征。