Author/Authors :
Ali, Akbar Knowledge Unit of Science - University of Management and Technology Sialkot 51310, Pakistan , Javaid, Mubeen Knowledge Unit of Science - University of Management and Technology Sialkot 51310, Pakistan , Matejic, Marjan Faculty of Electronic Engineering, 18000 Nis, Serbia , Milovanovic, Igor Faculty of Electronic Engineering, 18000 Nis, Serbia , Milovanovic, Emina Faculty of Electronic Engineering, 18000 Nis, Serbia
Abstract :
Let G = (V;E) be a simple connected graph with n vertices, m edges and
sequence of vertex degrees d1 ≥ d2 ≥ . . . . dn > 0, di = d(vi), where vi 2 V . With
i ∼ j we denote adjacency of vertices vi and vj . The general sum{connectivity index of
graph is defined as Χa(G) =P i∼j (di + dj )α, where α is an arbitrary real number. In
this paper we determine relations between Χα+β(G) and Χα+β1(G), where α and
are arbitrary real numbers, and obtain new bounds for Χα(G). Also, by the appropriate
choice of parameters α and , we obtain a number of old/new inequalities for different
vertex{degree{based topological indices.
