## ON ZAGREB INDICES OF DOUBLE VERTEX GRAPHS

## ON ZAGREB INDICES OF DOUBLE VERTEX GRAPHS

*S. S. Kumar, R. Sundareswaran, M. Sundarakannan*

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## 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.

## Keywords

Double vertex graph, Complete Double vertex graph, Zagreb Index, Hyper- Zagreb index.