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Open access

B. Basavanagoud, Veena R. Desai and Shreekant Patil


Let Eβ (G) be the set of paths of length β in a graph G. For an integer β ≥ 1 and a real number α, the (β,α)-connectivity index is defined as


The (2,1)-connectivity index shows good correlation with acentric factor of an octane isomers. In this paper, we compute the (2, α)-connectivity index of certain class of graphs, present the upper and lower bounds for (2, α)-connectivity index in terms of number of vertices, number of edges and minimum vertex degree and determine the extremal graphs which achieve the bounds. Further, we compute the (2, α)-connectivity index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC 4 C 8[p,q], tadpole graphs, wheel graphs and ladder graphs.

Open access

B. Basavanagoud, Wei Gao, Shreekant Patil, Veena R. Desai, Keerthi G. Mirajkar and B Pooja


For a (molecular) graph, the first Zagreb index is equal to the sum of squares of the degrees of vertices, and the F-index is equal to the sum of cubes of the degrees of vertices. In this paper, we introduce sixty four new operations on graphs and study the first Zagreb index and F-index of the resulting graphs.