Pancyclicity of Double Vertex Graph

Abstract

The double vertex graph U_2 (G) of a graph G of order n≥2 is the graph whose vertex set consists of all (n 2 ) unordered pairs of vertices of G and where two vertices {a,b} and {c,d} are adjacent if and only if |{a,b}∩{c,d}|=1 and if a=c, then b and d are adjacent in G. In this paper, we discuss some properties of U_2 (G) related to degree and distances. We also have obtained graphs G whose double vertex graphs contain G as a subgraph.