The PI index of phenylenes
The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n eu (e|G) and n ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ e∈E(G)[n eu (e|G) + n ev (e|G)], where n eu (e|G) is the number of edges of G lying closer to u than to v and n ev (e|...
| المؤلفون الرئيسيون: | , , |
|---|---|
| التنسيق: | Journal article |
| اللغة: | English |
| منشور في: |
Springer Netherlands
2006
|
| _version_ | 1826310727708704768 |
|---|---|
| author | Deng, H Chen, S Zhang, J |
| author_facet | Deng, H Chen, S Zhang, J |
| author_sort | Deng, H |
| collection | OXFORD |
| description | The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n eu (e|G) and n ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ e∈E(G)[n eu (e|G) + n ev (e|G)], where n eu (e|G) is the number of edges of G lying closer to u than to v and n ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of phenylenes is given, and a simple relation is established between the PI index of a phenylene and of the corresponding hexagonal squeeze. |
| first_indexed | 2024-03-07T07:56:16Z |
| format | Journal article |
| id | oxford-uuid:93728c08-2073-4bc3-88bb-7344ed076925 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:56:16Z |
| publishDate | 2006 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | oxford-uuid:93728c08-2073-4bc3-88bb-7344ed0769252023-08-17T11:48:45ZThe PI index of phenylenesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:93728c08-2073-4bc3-88bb-7344ed076925EnglishSymplectic Elements at OxfordSpringer Netherlands2006Deng, HChen, SZhang, JThe Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n eu (e|G) and n ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ e∈E(G)[n eu (e|G) + n ev (e|G)], where n eu (e|G) is the number of edges of G lying closer to u than to v and n ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of phenylenes is given, and a simple relation is established between the PI index of a phenylene and of the corresponding hexagonal squeeze. |
| spellingShingle | Deng, H Chen, S Zhang, J The PI index of phenylenes |
| title | The PI index of phenylenes |
| title_full | The PI index of phenylenes |
| title_fullStr | The PI index of phenylenes |
| title_full_unstemmed | The PI index of phenylenes |
| title_short | The PI index of phenylenes |
| title_sort | pi index of phenylenes |
| work_keys_str_mv | AT dengh thepiindexofphenylenes AT chens thepiindexofphenylenes AT zhangj thepiindexofphenylenes AT dengh piindexofphenylenes AT chens piindexofphenylenes AT zhangj piindexofphenylenes |