摘要：The degree subtraction matrix $DS(G)$ of a graph $G$ is introduced, whose $(j,k)$-th entry is $d_G(v_j) - d_G(v_k)$, where $d_G(v_j)$ is the degree of a vertex $v_j$ in $G$. If $G$ is a non-regular graph, then $DS(G)$ has exactly two nonzero eigenvalues which are purely imaginary. Eigenvalues of the degree subtraction matrices of a graph and of its complement are the same. The degree subtraction energy of $G$ is defined as the sum of absolute values of eigenvalues of $DS(G)$ and we express it in terms of the first Zagreb index.
关键词：Degree of a vertex; degree subtraction matrix; eigenvalues; energy; first Zagreb index.
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