The graphs, all of whose spanning trees are isomorphic to each other
Bohdan Zelinka
- Vol. 096, Iss: 1, pp 33-40
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The article was published on 1971-01-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Spanning tree.read more
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Book ChapterDOI
Finite and Infinite Graphs whose Spanning Trees are Pairwise Isomorphic
TL;DR: In this article, two new proofs of the theorem are given, one of which has the merit that it uses only the property that an isomorphism from one tree to another maps a path of length d to a path with length d. The other proof is by induction, and it rapidly shows that it is sufficient to examine the unicyclic graphs with the condition that every second vertex on the cycle has valency two.
Journal ArticleDOI
Graphs with all spanning trees nonisomorphic
TL;DR: It is proved that any such connected graph with at least two vertices must have the property that each end-block has just one edge, and it is shown that any graph is an induced subgraph of a connected graph without two distinct, isomorphic spanning trees.
Journal ArticleDOI
Graphs with two isomorphism classes of spanning unicyclic subgraphs
TL;DR: This work is a continuation of [6] where graphs with one isomorphism class of spanning unicyclic graphs are characterized.
Journal ArticleDOI
Two-cacti with minimum number of spanning trees
TL;DR: Zelinka (1978) proved that the spanning trees of a 2-cactus partition into at least 3 isomorphism classes, and here the structure of these 2- cacti is examined.
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