On Transmission Version of Laplacian Energy of a Graph

Let G be a graph with the vertices V(G) . The transmission of the vertex vi denoted by TR_G(V_i) is defined as the sum of distances between vi and any other vertices in G The Laplacian transmission matrix of G is defined as L_Tr(G). Thenthe transmission version of Laplacian energy of G is defined as LE_Tr(G). In this paper, we obtain some inequalities between LE_Tr(G) and other invariant of G like ordinary energy and Wiener and variable transmission Zagreb index