For a connected undirected graph G = (V;E) with vertex set {1; 2;: :: ; n} and degrees di, for 1≤ i≤ n, we show that ABC(G)≤ → (n-1)(|E|-R-1(G)); where R-1(G) = ∑ (i;j)ϵE 1/didj is the Randić index. This bound allows us to obtain some maximal results for the ABC index with elementary proofs and to improve all the upper bounds in [20], as well as some in [17], using lower bounds for R-1(G) found in the literature and some new ones found through the application of majorization.

Cornaro, A., Bianchi, M., Torriero, A., Palacios, J. (2016). New Upper Bounds for the ABC Index. MATCH, 76(1), 117-130.

New Upper Bounds for the ABC Index

Cornaro, Alessandra;Bianchi, Monica;Torriero, Anna;
2016

Abstract

For a connected undirected graph G = (V;E) with vertex set {1; 2;: :: ; n} and degrees di, for 1≤ i≤ n, we show that ABC(G)≤ → (n-1)(|E|-R-1(G)); where R-1(G) = ∑ (i;j)ϵE 1/didj is the Randić index. This bound allows us to obtain some maximal results for the ABC index with elementary proofs and to improve all the upper bounds in [20], as well as some in [17], using lower bounds for R-1(G) found in the literature and some new ones found through the application of majorization.
Articolo in rivista - Articolo scientifico
Atom-bond connectivity index; Randic index; Majorization; Schur-convex functions
English
2016
76
1
117
130
none
Cornaro, A., Bianchi, M., Torriero, A., Palacios, J. (2016). New Upper Bounds for the ABC Index. MATCH, 76(1), 117-130.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/334334
Citazioni
  • Scopus 20
  • ???jsp.display-item.citation.isi??? 18
Social impact