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.