Discussiones Mathematicae Graph Theory 28(3) (2008) 501-510
doi: 10.7151/dmgt.1423

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ON THE TREE GRAPH OF A CONNECTED GRAPH

Ana Paulina Figueroa

Instituto de Matemáticas
Universidad Nacional Autónoma de México
Ciudad Universitaria, México D.F. 04510, México

Eduardo Rivera-Campo

Departmento de Matemáticas
Universidad Autónoma Metropolitana-Iztapalapa
Av. San Rafael Atlixco 186, México D.F. 09340, México

Abstract

Let G be a graph and C be a set of cycles of G. The tree graph of G defined by C, is the graph T(G,C) that has one vertex for each spanning tree of G, in which two trees T and T′ are adjacent if their symmetric difference consists of two edges and the unique cycle contained in T∪T′ is an element of C. We give a necessary and sufficient condition for this graph to be connected for the case where every edge of G belongs to at most two cycles in C.

Keywords: tree graph, property Δ*, property Δ+.

2000 Mathematics Subject Classification: 05C05.

References

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Received 12 February 2008
Revised 18 June 2008
Accepted 18 June 2008