Some distance based indices of graphs based on four new operations related to the lexicographic product
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(...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2019-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/2106 |
| _version_ | 1819266397482516480 |
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| author | N. Dehgardi S.M. Sheikholeslami M. Soroudi |
| author_facet | N. Dehgardi S.M. Sheikholeslami M. Soroudi |
| author_sort | N. Dehgardi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T21:00:37Z |
| format | Article |
| id | doaj.art-238ed29317514226b04f5639d92645ca |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-23T21:00:37Z |
| publishDate | 2019-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-238ed29317514226b04f5639d92645ca2022-12-21T17:31:23ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102019-12-0111225826710.15330/cmp.11.2.258-2672106Some distance based indices of graphs based on four new operations related to the lexicographic productN. Dehgardi0S.M. Sheikholeslami1M. Soroudi2Department of Mathematics and Computer Science, Sirjan University of Technology, 7813733385, Sirjan, I.R. IranDepartment of Mathematics, Azarbaijan Shahid Madani University, 5375171379, Tabriz, I.R. IranDepartment of Mathematics, Azarbaijan Shahid Madani University, 5375171379, Tabriz, I.R. IranFor 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.https://journals.pnu.edu.ua/index.php/cmp/article/view/2106wiener indexdegree distance indexhyper-wiener indexlexicographic productsubdivisiontotal graph |
| spellingShingle | N. Dehgardi S.M. Sheikholeslami M. Soroudi Some distance based indices of graphs based on four new operations related to the lexicographic product Karpatsʹkì Matematičnì Publìkacìï wiener index degree distance index hyper-wiener index lexicographic product subdivision total graph |
| title | Some distance based indices of graphs based on four new operations related to the lexicographic product |
| title_full | Some distance based indices of graphs based on four new operations related to the lexicographic product |
| title_fullStr | Some distance based indices of graphs based on four new operations related to the lexicographic product |
| title_full_unstemmed | Some distance based indices of graphs based on four new operations related to the lexicographic product |
| title_short | Some distance based indices of graphs based on four new operations related to the lexicographic product |
| title_sort | some distance based indices of graphs based on four new operations related to the lexicographic product |
| topic | wiener index degree distance index hyper-wiener index lexicographic product subdivision total graph |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/2106 |
| work_keys_str_mv | AT ndehgardi somedistancebasedindicesofgraphsbasedonfournewoperationsrelatedtothelexicographicproduct AT smsheikholeslami somedistancebasedindicesofgraphsbasedonfournewoperationsrelatedtothelexicographicproduct AT msoroudi somedistancebasedindicesofgraphsbasedonfournewoperationsrelatedtothelexicographicproduct |