463:
457:
327:
187:
134:
333:
366:
482:
Padmakar, V. Khadikar.; Sneha, Karmarkar; Vijay K., Agrawal (2001), "A Novel PI Index and Its
Applications to QSPR/QSAR Studies",
557:
207:
567:
517:
Khalifeh, M.H.; Darafsheh, M.R; Jolany, H. (2011), "The Wiener, Szeged, and PI Indices of a
Dendrimer Nanostar",
562:
40:
20:
526:
147:
94:
341:
499:
28:
534:
491:
452:{\displaystyle \operatorname {PI} (G_{n})=441\cdot 4^{n}-639\cdot 2^{n}+232,\quad n\geq 0.}
530:
349:
44:
551:
52:
48:
36:
462:
360:
The PI index of
Dendrimer Nanostar of the following figure can be calculated by
345:
538:
503:
337:
32:
495:
461:
39:. The Padmakar–Ivan index is a generalization introduced by
322:{\displaystyle \operatorname {PI} (G)=\sum _{e\in E(G)}}
136:
denotes the number of edges lying closer to the vertex
369:
210:
150:
97:
519:
451:
321:
189:is the number of edges lying closer to the vertex
181:
128:
67:of number of edges which are not equidistant from
332:The PI index is very important in the study of
8:
334:quantitative structure–activity relationship
336:for the classification models used in the
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405:
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368:
292:
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233:
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155:
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102:
96:
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197:. The Padmakar–Ivan index of a graph
55:. The Padmakar–Ivan index of a graph
7:
14:
439:
182:{\displaystyle n_{ev}(e\mid G)}
129:{\displaystyle n_{eu}(e\mid G)}
389:
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316:
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1:
59:is the sum over all edges
584:
484:J. Chem. Inf. Comput. Sci.
25:Padmakar–Ivan (PI) index
558:Mathematical chemistry
539:10.1166/jctn.2011.1681
466:
453:
323:
183:
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47:of the concept of the
465:
454:
324:
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21:chemical graph theory
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41:Padmakar V. Khadikar
16:Concept in chemistry
531:2011JCTN....8..220K
342:biological sciences
467:
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319:
253:
179:
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496:10.1021/ci0003092
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29:topological index
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568:Graph invariants
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193:than the vertex
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186:
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140:than the vertex
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110:
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51:, introduced by
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563:Cheminformatics
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365:
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358:
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257:
206:
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151:
146:
145:
98:
93:
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79:be a graph and
17:
12:
11:
5:
581:
579:
571:
570:
565:
560:
550:
549:
545:
544:
525:(2): 220–223,
509:
490:(4): 934–949,
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350:nanotechnology
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201:is defined as
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125:
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15:
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10:
9:
6:
4:
3:
2:
580:
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540:
536:
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83: =
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198:
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141:
137:
88:
84:
80:
76:
72:
68:
64:
60:
56:
53:Harry Wiener
49:Wiener index
37:biochemistry
24:
18:
346:engineering
87:an edge of
45:Iván Gutman
552:Categories
470:References
35:, used in
444:≥
418:⋅
412:−
399:⋅
374:
308:∣
277:∣
238:∈
231:∑
215:
171:∣
118:∣
504:11500110
356:Examples
338:chemical
33:molecule
527:Bibcode
91:. Here
502:
348:, and
144:, and
75:. Let
23:, the
31:of a
27:is a
500:PMID
71:and
63:of
43:and
535:doi
492:doi
434:232
415:639
396:441
19:In
554::
533:,
521:,
498:,
488:41
486:,
447:0.
371:PI
352:.
344:,
340:,
212:PI
85:uv
61:uv
542:.
537::
529::
523:8
507:.
494::
441:n
437:,
431:+
426:n
422:2
407:n
403:4
393:=
390:)
385:n
381:G
377:(
317:]
314:)
311:G
305:e
302:(
297:v
294:e
290:n
286:+
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280:G
274:e
271:(
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259:n
255:[
250:)
247:G
244:(
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235:e
227:=
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221:G
218:(
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191:v
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174:G
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165:(
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115:e
112:(
107:u
104:e
100:n
89:G
81:e
77:G
73:v
69:u
65:G
57:G
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