Let G be a graph. The energy of G, E(G)$\mathcal{E}(G)$$\mathcal{E}(G)$, is defined as the sum of absolute values of its eigenvalues. Here, it is shown that if G is a graph and {H1,…,Hk}$\{H_1,\dots ,H_k\}$$\{H_1,\dots ,H_k\}$ is an edge partition of G, such that H1,…,Hk$H_1,\dots ,H_k$$H_1,\dots ,H_k$ are spanning; then E(G)=∑ki=1E(Hi)$\mathcal{E}(G)=\sum _{i=1}^k\mathcal{E}(H_i)$$\mathcal{E}(G)=\sum _{i=1}^k\mathcal{E}(H_i)$ if and only if AiAj=0$A_i{A}_j=0$, for every $1⩽i,j⩽k$ and $i\ne j$, where $A_i$ is the adjacency matrix of $H_i$. It was proved that if G is a graph and $H_1,\dots ,H_k$ are subgraphs of G which partition edges of G, then $\mathcal{E}(G)⩽\sum _{i=1}^k\mathcal{E}(H_i)$. In this paper we show that if G is connected, then the equality is strict, that is $\mathcal{E}(G)<\sum _{i=1}^k\mathcal{E}(H_i)$.

设G是一个图。G的能量，乙( G )$\mathcal{乙}（G）$$\mathcal{E}(G)$，被定义为其特征值的绝对值之和。这里表明，如果G是一个图并且{H1, … ,Hk}$\{H_1,\dots \dots ,H_k\}$$\{H_1,\dots ,H_k\}$是G的边划分，使得H1, … ,Hk$H_1,\dots \dots ,H_k$$H_1,\dots ,H_k$正在跨越；然后乙( G ) =Σk我= 1乙（H我）$\mathcal{乙}（G）=\underset{我=1}{\overset{k}{\Sigma }}\mathcal{乙}（H_{我}）$$\mathcal{E}(G)=\sum _{i=1}^k\mathcal{E}(H_i)$当且仅当A i A j = 0$A_i{A}_j=0$，对于每一个$1⩽我,j⩽k$和$我\ne j$， 在哪里$A_{我}$是的邻接矩阵$H_{我}$。证明了如果G是一个图且$H_1,\dots \dots ,H_k$是G的子图，其划分G的边，然后$\mathcal{乙}（G）⩽\underset{我=1}{\overset{k}{\Sigma }}\mathcal{乙}（H_{我}）$。在本文中我们证明如果G是连通的，那么等式是严格的，即$\mathcal{乙}（G）<\underset{我=1}{\overset{k}{\Sigma }}\mathcal{乙}（H_{我}）$。