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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 764.05077

**Autor: ** Alavi, Yousef; Behzad, Mehdi; Erdös, Paul; Lick, Don R.

**Title: ** Double vertex graphs. (In English)

**Source: ** J. Comb. Inf. Syst. Sci. 16, No.1, 37-50 (1991).

**Review: ** Let G be a (V,E) graph of order p \geq 2. The double vertex graph V_{2}(G) of 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**}**\cap**{**u,v**}**| = 1 and if x = u, then y and v are adjacent in G. For this class of graphs we develop basic properties and study regular, eulerian, bipartite graphs, as well as general structural properties of these graphs.

**Classif.: ** * 05C75 Structural characterization of types of graphs

05C45 Eulerian and Hamiltonian graphs

05C40 Connectivity

**Keywords: ** regular graph; Eulerian graph; double vertex graph; bipartite graphs

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