@article{Dehgardi_Sheikholeslami_Soroudi_2019, title={Some distance based indices of graphs based on four new operations related to the lexicographic product}, volume={11}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/2106}, DOI={10.15330/cmp.11.2.258-267}, abstractNote={<p>For a (molecular) graph, the Wiener index, hyper-Wiener index and degree distance index are defined as $$W(G)= \sum_{\{u,v\}\subseteq V(G)}d_G(u,v),$$ $$WW(G)=W(G)+\sum_{\{u,v\}\subseteq V(G)} d_{G}(u,v)^2,$$ and $$DD(G)=\sum_{\{u,v\}\subseteq V(G)}d_G(u, v)(d(u/G)+d(v/G)),$$ respectively, where $d(u/G)$ denotes the degree of a vertex $u$ in $G$ and $d_G(u, v)$ is distance between two vertices $u$ and $v$ of a graph $G$. In this paper, we study Wiener index, hyper-Wiener index and degree distance index of graphs based on four new operations related to the lexicographic product, subdivision and total graph.</p>}, number={2}, journal={Carpathian Mathematical Publications}, author={Dehgardi, N. and Sheikholeslami, S.M. and Soroudi, M.}, year={2019}, month={Dec.}, pages={258–267} }