On Some Vertex-Degree-Based Graph Invariants

Let G = (V,E) be a graph, du the degree of its vertex u , and uv the edge connecting the vertices u and v . The atom–bond connectivity index and the sum–connectivity index of G are defined as ABC = ∑ uv∈E √ (du + dv − 2)/(du dv) and χ = ∑ uv∈E 1/ √ du + dv , respectively. Continuing the recent researches on ABC [B. Furtula, A. Graovac, D. Vukicevic, Atom-bond connectivity index of trees, Discr. Appl. Math. 157 (2009) 2828–2835] and χ [B. Zhou, N. Trinajstic, On a novel connectivity index, J. Math. Chem. 46 (2009) 1252–1270] we obtain novel upper bounds on these vertex–degree–based graph invariants.