Open AccessSome distance based indices of graphs based on four new operations related to the lexicographic product
Author(s) -
Nasrin Dehgardi,
Seyed Mahmoud Sheikholeslami,
Marzieh Soroudi
Publication year - 2019
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.11.2.258-267
Subject(s) - wiener index , mathematics , combinatorics , lexicographical order , vertex (graph theory) , graph , product (mathematics) , connectivity , index (typography) , degree (music) , geometry , physics , world wide web , computer science , acoustics
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.