Some lower and upper bounds on the third ABC index
Atom-bond connectivity (ABC) index has been applied up to now to study the stability of alkanes and the strain energy of cycloalkanes. Graovac defined the second ABC index as ABC2(G)=∑vivj∈E(G)1ni+1nj−2ninj, and Kinkar studied the upper bounds. In this paper, we define a new index which is called th...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2016-04-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860016000050 |
| _version_ | 1818117187383066624 |
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| author | Dae-Won Lee |
| author_facet | Dae-Won Lee |
| author_sort | Dae-Won Lee |
| collection | DOAJ |
| description | Atom-bond connectivity (ABC) index has been applied up to now to study the stability of alkanes and the strain energy of cycloalkanes. Graovac defined the second ABC index as
ABC2(G)=∑vivj∈E(G)1ni+1nj−2ninj,
and Kinkar studied the upper bounds. In this paper, we define a new index which is called the third ABC index and it is defined as
(1) ABC3(G)=∑vivj∈E(G)1ei+1ej−2eiej,
and we present some lower and upper bounds on ABC3 index of graphs. |
| first_indexed | 2024-12-11T04:34:25Z |
| format | Article |
| id | doaj.art-5fd209ec39ef4cc88e8907697e7e91ab |
| institution | Directory Open Access Journal |
| issn | 0972-8600 |
| language | English |
| last_indexed | 2024-12-11T04:34:25Z |
| publishDate | 2016-04-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-5fd209ec39ef4cc88e8907697e7e91ab2022-12-22T01:20:46ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002016-04-01131111510.1016/j.akcej.2016.02.002Some lower and upper bounds on the third ABC indexDae-Won LeeAtom-bond connectivity (ABC) index has been applied up to now to study the stability of alkanes and the strain energy of cycloalkanes. Graovac defined the second ABC index as ABC2(G)=∑vivj∈E(G)1ni+1nj−2ninj, and Kinkar studied the upper bounds. In this paper, we define a new index which is called the third ABC index and it is defined as (1) ABC3(G)=∑vivj∈E(G)1ei+1ej−2eiej, and we present some lower and upper bounds on ABC3 index of graphs.http://www.sciencedirect.com/science/article/pii/S0972860016000050Molecular graphAtom-bond connectivity (ABC) indexThe third Atom-bond connectivity (ABC3) indexTopological indices |
| spellingShingle | Dae-Won Lee Some lower and upper bounds on the third ABC index AKCE International Journal of Graphs and Combinatorics Molecular graph Atom-bond connectivity (ABC) index The third Atom-bond connectivity (ABC3) index Topological indices |
| title | Some lower and upper bounds on the third ABC index |
| title_full | Some lower and upper bounds on the third ABC index |
| title_fullStr | Some lower and upper bounds on the third ABC index |
| title_full_unstemmed | Some lower and upper bounds on the third ABC index |
| title_short | Some lower and upper bounds on the third ABC index |
| title_sort | some lower and upper bounds on the third abc index |
| topic | Molecular graph Atom-bond connectivity (ABC) index The third Atom-bond connectivity (ABC3) index Topological indices |
| url | http://www.sciencedirect.com/science/article/pii/S0972860016000050 |
| work_keys_str_mv | AT daewonlee somelowerandupperboundsonthethirdabcindex |