ON ARITHMETIC-GEOMETRIC AND GEOMETRIC-ARITHMETIC INDICES OF GRAPHS

Let G be a connected graph having vertex set {v1, ... ,vn} and vertex-degree sequence (d1, ... ,dn), where di represents the degree of the vertex vi . If the vertices vi and vj are adjacent in G, we write i similar to j. The arithmetic-geometric index and the geometric-arithmetic index of G are defined as AG(G) = n-ary sumation i similar to j[(di +dj)/(2Vdidj)] and GA(G) = n-ary sumation i similar to j[2Vdidj/(di +dj)], respectively. Since AG(G) and GA(G) are closely related quantities, we derive bounds on their addition as well as on their difference, namely on irrAG(G) = AG(G) - GA(G) and r(G) = AG(G) + GA(G). Some new bounds on AG(G) are also obtained.