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.
Let G = (V,E) be a simple connected graph. The diameter of a connected graph G is denoted by diam(G) and is the maximum eccentricity in a graph G. In this article, we establish the results for diameter of Middle graph [M(G)] of a graph G and the equality relation between the diameter of graph G, Middle graph [M(G)] and Total graph [T(G)] of a graph G.
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