Bounds for the augmented Zagreb index
The augmented Zagreb index (\rm{AZI} for short) of a graph $G$, introduced by Furtula et al. in 2010, is defined as ${\rm AZI}(G)=\sum\limits_{v_iv_j\in E(G)}{\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)}^3$, where $E(G)$ is the edge set of $G$, and $d(v_i)$ denotes the degree of the vertex $v_...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Georgia Southern University
2023-01-01
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| Series: | Theory and Applications of Graphs |
| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/10/ |
| _version_ | 1797833794084929536 |
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| author | Ren qingcuo Li Wen Suonan Renqian Yang Chenxu |
| author_facet | Ren qingcuo Li Wen Suonan Renqian Yang Chenxu |
| author_sort | Ren qingcuo |
| collection | DOAJ |
| description | The augmented Zagreb index (\rm{AZI} for short) of a graph $G$, introduced by Furtula et al. in 2010, is defined as ${\rm AZI}(G)=\sum\limits_{v_iv_j\in E(G)}{\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)}^3$, where $E(G)$ is the edge set of $G$, and $d(v_i)$ denotes the degree of the vertex $v_i$. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs. \\[2mm] {\bf Keywords:} Agumented Zagreb index; molecular trees; Triangle-free graph |
| first_indexed | 2024-04-09T14:29:50Z |
| format | Article |
| id | doaj.art-da96f2c21e644c439bb36780dd701294 |
| institution | Directory Open Access Journal |
| issn | 2470-9859 |
| language | English |
| last_indexed | 2024-04-09T14:29:50Z |
| publishDate | 2023-01-01 |
| publisher | Georgia Southern University |
| record_format | Article |
| series | Theory and Applications of Graphs |
| spelling | doaj.art-da96f2c21e644c439bb36780dd7012942023-05-03T17:30:20ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592023-01-0110111010.20429/tag.2023.10110Bounds for the augmented Zagreb indexRen qingcuoLi WenSuonan RenqianYang ChenxuThe augmented Zagreb index (\rm{AZI} for short) of a graph $G$, introduced by Furtula et al. in 2010, is defined as ${\rm AZI}(G)=\sum\limits_{v_iv_j\in E(G)}{\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)}^3$, where $E(G)$ is the edge set of $G$, and $d(v_i)$ denotes the degree of the vertex $v_i$. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs. \\[2mm] {\bf Keywords:} Agumented Zagreb index; molecular trees; Triangle-free graphhttps://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/10/ |
| spellingShingle | Ren qingcuo Li Wen Suonan Renqian Yang Chenxu Bounds for the augmented Zagreb index Theory and Applications of Graphs |
| title | Bounds for the augmented Zagreb index |
| title_full | Bounds for the augmented Zagreb index |
| title_fullStr | Bounds for the augmented Zagreb index |
| title_full_unstemmed | Bounds for the augmented Zagreb index |
| title_short | Bounds for the augmented Zagreb index |
| title_sort | bounds for the augmented zagreb index |
| url | https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/10/ |
| work_keys_str_mv | AT renqingcuo boundsfortheaugmentedzagrebindex AT liwen boundsfortheaugmentedzagrebindex AT suonanrenqian boundsfortheaugmentedzagrebindex AT yangchenxu boundsfortheaugmentedzagrebindex |