TY - JOUR
AU - Dehgardi, N.
AU - Sheikholeslami, S.M.
AU - Soroudi, M.
PY - 2019/12/31
Y2 - 2024/05/24
TI - Some distance based indices of graphs based on four new operations related to the lexicographic product
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 11
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.11.2.258-267
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/2106
SP - 258-267
AB - <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>
ER -