New Upper Bounds for the ABC Index

作者：Bianchi Monica; Cornaro Alessandra; Palacios Jose Luis; Torriero Anna

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2016, 76(1): 117-130.

For a connected undirected graph G = (V, E) with vertex set {1, 2, ..., n} and degrees d(i), for 1 <= i <= n, we show that
ABC(G) <= root(n - 1)(vertical bar E vertical bar - R-1(G)),
where R-1(G) = Sigma((i,j)is an element of E) 1/d(i)d(j) is the Randic 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.

• 出版日期2016