Some graft transformations and their applications on distance (signless) Laplacian spectra of graphs

Dandy Fan, Guoping Wang

Suppose that the vertex set of a connected graph $G$ is $V(G)=\{v_1,\cdots ,v_n\}$. Then we denote by $T{r}_G(v_i)$ the sum of distances between $v_i$ and all other vertices of $G$.…