A Proof of a Conjecture on the Distance Spectral Radius and Maximum Transmission of Graphs

Let G be a simple connected graph, and D(G) the distance matrix of G. Suppose that $$D_{\max }(G)$$ $$\lambda _1(G)$$ are maximum row sum spectral radius D(G), respectively. In this paper, we give lower bound for }(G)-\lambda , characterize extremal graphs attaining bound. As corollary, solve conjecture posed by Liu, Shu Xue.