A simple approach to order the multiplicative Zagreb indices of connected graphs
The first ($Pi_1$) and the second $(Pi_2$) multiplicative Zagreb indices of a connected graph $G$, with vertex set $V(G)$ and edge set $E(G)$, are defined as $Pi_1(G) = prod_{u in V(G)} {d_u}^2$ and $Pi_2(G) = prod_{uv in E(G)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the verte...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2012-12-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | http://www.combinatorics.ir/?_action=showPDF&article=2146&_ob=61a92ef69e13895fcd946bfe86a93cd7&fileName=full_text.pdf. |
| _version_ | 1828330794923327488 |
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| author | Mehdi Eliasi |
| author_facet | Mehdi Eliasi |
| author_sort | Mehdi Eliasi |
| collection | DOAJ |
| description | The first ($Pi_1$) and the second $(Pi_2$) multiplicative Zagreb indices of a connected graph $G$, with vertex set $V(G)$ and edge set $E(G)$, are defined as $Pi_1(G) = prod_{u in V(G)} {d_u}^2$ and $Pi_2(G) = prod_{uv in E(G)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. In this paper we present a simple approach to order these indices for connected graphs on the same number of vertices. Moreover, as an application of this simple approach, we extend the known ordering of the first and the second multiplicative Zagreb indices for some classes of connected graphs. |
| first_indexed | 2024-04-13T20:44:44Z |
| format | Article |
| id | doaj.art-b3c3b241ca54433cad378e9cdb809de4 |
| institution | Directory Open Access Journal |
| issn | 2251-8657 2251-8665 |
| language | English |
| last_indexed | 2024-04-13T20:44:44Z |
| publishDate | 2012-12-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | Transactions on Combinatorics |
| spelling | doaj.art-b3c3b241ca54433cad378e9cdb809de42022-12-22T02:30:44ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652012-12-01141724A simple approach to order the multiplicative Zagreb indices of connected graphsMehdi EliasiThe first ($Pi_1$) and the second $(Pi_2$) multiplicative Zagreb indices of a connected graph $G$, with vertex set $V(G)$ and edge set $E(G)$, are defined as $Pi_1(G) = prod_{u in V(G)} {d_u}^2$ and $Pi_2(G) = prod_{uv in E(G)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. In this paper we present a simple approach to order these indices for connected graphs on the same number of vertices. Moreover, as an application of this simple approach, we extend the known ordering of the first and the second multiplicative Zagreb indices for some classes of connected graphs.http://www.combinatorics.ir/?_action=showPDF&article=2146&_ob=61a92ef69e13895fcd946bfe86a93cd7&fileName=full_text.pdf.multiplicative Zagreb indexmajorizationunicyclic graphsbicyclic graphs |
| spellingShingle | Mehdi Eliasi A simple approach to order the multiplicative Zagreb indices of connected graphs Transactions on Combinatorics multiplicative Zagreb index majorization unicyclic graphs bicyclic graphs |
| title | A simple approach to order the multiplicative Zagreb indices of connected graphs |
| title_full | A simple approach to order the multiplicative Zagreb indices of connected graphs |
| title_fullStr | A simple approach to order the multiplicative Zagreb indices of connected graphs |
| title_full_unstemmed | A simple approach to order the multiplicative Zagreb indices of connected graphs |
| title_short | A simple approach to order the multiplicative Zagreb indices of connected graphs |
| title_sort | simple approach to order the multiplicative zagreb indices of connected graphs |
| topic | multiplicative Zagreb index majorization unicyclic graphs bicyclic graphs |
| url | http://www.combinatorics.ir/?_action=showPDF&article=2146&_ob=61a92ef69e13895fcd946bfe86a93cd7&fileName=full_text.pdf. |
| work_keys_str_mv | AT mehdieliasi asimpleapproachtoorderthemultiplicativezagrebindicesofconnectedgraphs AT mehdieliasi simpleapproachtoorderthemultiplicativezagrebindicesofconnectedgraphs |