On a transmission version of signless Laplacian energy of graphs

Let G be a graph with the vertex set V (G) = {v۱,..., vn}. The transmission of the vertex vi ϵ V (G),denoted by G(vi), is de ned to be the sum of distances between vi and any other vertices in G , i.e., G(vi) = = dG(vi, vj ). The signless Laplacian transmission matrix of G is de ned as L+Tr(G) =diag( αG(v۱),... ,α G(vn)) + A(G), where A(G) is the adjacency matrix of G. Let q۱ + ,... , q۱ + be theeigenvalues of LTr + (G). Then a transmission version of Laplacian energy of G is de ned as EL Tr + (G) =i=۱ n μ i + - ۲W(G)/n . In this paper, we aim to obtain some bounds for EL Tr + (G) in terms of other invariantsof G like, ordinary energy, Wiener and variable transmission Zagreb index.

کلیدواژه ها:

Transmission ، Eigenvalue ، Energy (of graph) ، signless Laplacian matrix