A characterization of extremal non-transmission-regular graphs by the distance (signless Laplacian) spectral radius

Jingfen Lan, Lele Liu

Let $G$ be a simple connected graph of order $n$ and $\partial (G)$ is the spectral radius of the distance matrix $D(G)$ of $G$. The transmission $D_i$ of vertex $i$ is the $i$-th r…