PI INDEX OF SOME BENZENOID GRAPHS

PI INDEX OF SOME BENZENOID GRAPHS

The Padmakar-Ivan (PI) index of a graph G is defined as PI(G) = ∑[neu(e|G)+ n ev(e|G)], where neu(e|G) is the number of edges of G lying closer to u than to v, n ev(e|G) is the number of edges of G lying closer to v than to u and summation goes over all edges of G. In this paper, we first...

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Autores principales: REZA ASHRAFI,ALI, LOGHMAN,AMIR
Lenguaje:English
Publicado: Sociedad Chilena de Química 2006
Materias:
Topological index
PI index
Benzenoid graph
molecular graph
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072006000300008
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spelling oai:scielo:S0717-970720060003000082006-11-16PI INDEX OF SOME BENZENOID GRAPHSREZA ASHRAFI,ALILOGHMAN,AMIR Topological index PI index Benzenoid graph molecular graph The Padmakar-Ivan (PI) index of a graph G is defined as PI(G) = ∑[neu(e|G)+ n ev(e|G)], where neu(e|G) is the number of edges of G lying closer to u than to v, n ev(e|G) is the number of edges of G lying closer to v than to u and summation goes over all edges of G. In this paper, we first compute the PI index of a class of pericondensed benzenoid graphs consisting of n rows, n ≤ 3, of hexagons of various lengths. Finally, we prove that for any connected graph G with exactly m edges, PI(G) ≤ m(m-1) with equality if and only if G is an acyclic graph or a cycle of odd lengthinfo:eu-repo/semantics/openAccessSociedad Chilena de QuímicaJournal of the Chilean Chemical Society v.51 n.3 20062006-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072006000300008en10.4067/S0717-97072006000300008
institution Scielo Chile
collection Scielo Chile
language English
topic Topological index
PI index
Benzenoid graph
molecular graph
spellingShingle Topological index
PI index
Benzenoid graph
molecular graph
REZA ASHRAFI,ALI
LOGHMAN,AMIR
PI INDEX OF SOME BENZENOID GRAPHS
description The Padmakar-Ivan (PI) index of a graph G is defined as PI(G) = ∑[neu(e|G)+ n ev(e|G)], where neu(e|G) is the number of edges of G lying closer to u than to v, n ev(e|G) is the number of edges of G lying closer to v than to u and summation goes over all edges of G. In this paper, we first compute the PI index of a class of pericondensed benzenoid graphs consisting of n rows, n ≤ 3, of hexagons of various lengths. Finally, we prove that for any connected graph G with exactly m edges, PI(G) ≤ m(m-1) with equality if and only if G is an acyclic graph or a cycle of odd length
author REZA ASHRAFI,ALI
LOGHMAN,AMIR
author_facet REZA ASHRAFI,ALI
LOGHMAN,AMIR
author_sort REZA ASHRAFI,ALI
title PI INDEX OF SOME BENZENOID GRAPHS
title_short PI INDEX OF SOME BENZENOID GRAPHS
title_full PI INDEX OF SOME BENZENOID GRAPHS
title_fullStr PI INDEX OF SOME BENZENOID GRAPHS
title_full_unstemmed PI INDEX OF SOME BENZENOID GRAPHS
title_sort pi index of some benzenoid graphs
publisher Sociedad Chilena de Química
publishDate 2006
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072006000300008
work_keys_str_mv AT rezaashrafiali piindexofsomebenzenoidgraphs
AT loghmanamir piindexofsomebenzenoidgraphs
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