Pi index of some benzenoid graphs

• ALI REZA ASHRAFI ^[1] ; AMIR LOGHMAN ^[1]
  1. [1] University of Kashan

     University of Kashan

     Irán

     
• Localización: Journal of the Chilean Chemical Society (Boletín de la Sociedad Chilena de Química), ISSN-e 0717-6309, ISSN 0366-1644, Vol. 51, Nº. 3, 2006, págs. 968-970
• Idioma: inglés
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• Resumen

  • 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