On zagreb indices of double vertex graphs

Abstract

Let G = (V, E) be a graph with at least 2 vertices, then the double vertex graph U₂(G) is the graph whose vertex set consists of all 2-subsets of V such that two distinct vertices {x, y} and {u, v} are adjacent if and only if |{x, y} ∩ {u, v}| = 1 and if x = u, then y and v are adjacent in G. Similarly, the complete double vertex graph, denoted by CU₂(G), has vertex set consists of all unordered pairs of elements of V and two distinct vertices {x, y} and {u, v} are adjacent if and only if |{x, y} ∩ {u, v}| = 1 and if x = u, then y and v are adjacent in G. In this work, we compute the zagreb indices of double vertex and complete double vertex graphs.