@article {IOPORT.00867728,
    author       = {Vince, Andrew and Yang, Yongzhi},
    title        = {Reconstruction of the set of branches of a graph.},
    year         = {1996},
    journal      = {Graphs and Combinatorics},
    volume       = {12},
    number       = {1},
    issn         = {0911-0119},
    pages        = {69-80},
    publisher    = {Springer-Verlag, Tokyo},
    doi          = {10.1007/BF01858446},
    abstract     = {A $k$-vertex in a graph is a vertex of degree $k$. The pruned graph $\text {pruned} (G)$ of a separable graph $G$ is the maximal subgraph of $G$ having no 1-vertex. The block or cutpoint $P$ of $G$ which corresponds to the center of the block-cutpoint tree of $\text {pruned} (G)$ is called the pruned center of $G$. A branch $B$ of $G$ is a maximal subgraph of $G$ that contains exactly one vertex $u$ of the pruned center $P$ such that $B - u$ is connected. The reconstruction of the branches of $G$ plays an important role in the reconstruction of $G$. In this paper the authors improve upon a result of {\it D. L. Greenwell} and {\it R. L. Hemminger} [Many Facets of Graph Theory, Proc. Conf. Western Michigan Univ., Kalamazoo/Mi. 1968, 91-114 (1969; Zbl 0187.45601)] and prove that the branches of $G$ are reconstructible except when all the following conditions hold: (i) $\text{pruned} (G)$ is a vertex or an edge, (ii) $G$ has exactly two branches, and (iii) one branch contains all 1-vertices of $G$ and the other branch contains exactly one end-block. Further, they prove that in the extended case, the reconstruction of the branches is equivalent to the reconstruction of the graph itself. A related reference on reconstruction of separable graphs is [{\it V. Krishnamoorthy} and {\it K. R. Parthasarathy}, On the reconstruction conjecture for separable graphs, J. Aust. Math. Soc., Ser. A 30, 307-320 (1981; Zbl 0472.05047)].},
    reviewer     = {K.R.Parthasarathy (Narayanapuram)},
    identifier   = {00867728},
}