GA2 index of some graph operations

Let G = (V, E) be a graph. For e = uv ∈ E(G), nu (e) is the number of vertices of G lying closer to u than to v and nv (e) is the number of vertices of G lying closer to v than u. The GA2 index of G is defined as ∑uv∈E(G) 2√ nu(e)nv(e) / nu(e) + nv(e). We explore here some mathematical properties and present explicit formulas for this new index under several graph operations. 2010 Mathematics Subject Classifications. 05C12, 05A15, 05A20, 05C05. .

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