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 V2(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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