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
117
130
14
Cornaro, A., Bianchi, M., Torriero, A., & Palacios, J. (2016). New Upper Bounds for the ABC Index. MATCH, 76(1), 117-130.
Cornaro, A; Bianchi, M; Torriero, A; Palacios, J
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/334334
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