A Unified Approach to Extremal Trees with Respect to Geometric-Arithmetic, Szeged and Edge Szeged Indices

作者：Hua, Hongbo^*; Zhang, Shenggui

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2011, 65(3): 691-704.

The second and third geometric-arithmetic indices GA(2)(G) and GA(3)(G) of a graph G are defined, respectively, as Sigma(uv is an element of E(G)) root n(u)(e,G)n(v)(e,G)/1/2[n(u)(e,G)+n(v)(e,G)] and Sigma(uv is an element of E(G)) root m(u)(e,G)m(v)(e,G)/1/2[m(u)(e,G)+m(v)(e,G)] , where e = uv is one edge in G, n(u)(e, G) denotes the number of vertices in G lying closer to u than to v and m(u)(e,G) denotes the number of edges in G lying closer to u than to v. The Szeged and edge Szeged indices are defined, respectively, as Sz(G) = Sigma(uv is an element of E(G)) n(u)(e, G) . n(v) (e, G) and Sz(e)(G) = Sigma(uv is an element of E(G)) m(u)(e, G) . m(v)(e, G). In this paper, we provide a unified approach to characterize the tree with the minimum and maximum GA(2), GA(3), Sz and Sz(e) indices among the set of trees with given order and pendent vertices, respectively. As applications, we deduce a result of [2] concerning tree with the maximum GA(2) index and a result of [3] concerning tree with the maximum GA(3) index.

• 出版日期2011
• 单位西北工业大学; 淮阴工学院