# On the tree graph of a connected graph

Ana Paulina Figueroa; Eduardo Rivera-Campo

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 3, page 501-510
- ISSN: 2083-5892

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topAna Paulina Figueroa, and Eduardo Rivera-Campo. "On the tree graph of a connected graph." Discussiones Mathematicae Graph Theory 28.3 (2008): 501-510. <http://eudml.org/doc/270574>.

@article{AnaPaulinaFigueroa2008,

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.},

author = {Ana Paulina Figueroa, Eduardo Rivera-Campo},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {tree graph; property Δ*; property Δ⁺; property ; property },

language = {eng},

number = {3},

pages = {501-510},

title = {On the tree graph of a connected graph},

url = {http://eudml.org/doc/270574},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Ana Paulina Figueroa

AU - Eduardo Rivera-Campo

TI - On the tree graph of a connected graph

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 3

SP - 501

EP - 510

AB - 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.

LA - eng

KW - tree graph; property Δ*; property Δ⁺; property ; property

UR - http://eudml.org/doc/270574

ER -

## References

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- [2] F. Harary, R.J. Mokken and M. Plantholt, Interpolation theorem for diameters of spanning trees, IEEE Trans. Circuits and Systems 30 (1983) 429-432, doi: 10.1109/TCS.1983.1085385. Zbl0528.05019
- [3] K. Heinrich and G. Liu, A lower bound on the number of spanning trees with k endvertices, J. Graph Theory 12 (1988) 95-100, doi: 10.1002/jgt.3190120110. Zbl0655.05038
- [4] X. Li, V. Neumann-Lara and E. Rivera-Campo, On a tree graph defined by a set of cycles, Discrete Math. 271 (2003) 303-310, doi: 10.1016/S0012-365X(03)00132-8. Zbl1021.05025
- [5] F.J. Zhang and Z. Chen, Connectivity of (adjacency) tree graphs, J. Xinjiang Univ. Natur. Sci. 3 (1986) 1-5. Zbl0645.05031

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