Abstract
Because of the widespread applications of tree and tree graph in computer science, we are interested in studying the tree graph. M. Farber, B. Richter and H. Shank in [1] showed that the graph τ2 (G) is connected. The result of this paper is: graph τ2(G) is 2-edge-connected as |V(G) ≥3, at the same time, we will show the best lower bounds about vertex number and minimum degree of graph τ2(G).
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References
M. Farber, B. Richter and H. Shank, Edge-disjoint spanning trees: A connected ness theorem,Journal of Graph Theorem,9:3(1985).
R. L. Cummins, Hamilton circuits in tree graphs,IEEE Trans Circuit Theory, CT-13 (1966), 82–90.
H. Shank, A note on hamilton circuits in tree graph,IEEE Trans. Circuit Theory, CT-15 (1986).
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Li, H., Liu, Q. A problem of tree graph. J. of Comput. Sci. & Technol. 4, 61–66 (1989). https://doi.org/10.1007/BF02943989
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DOI: https://doi.org/10.1007/BF02943989