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### 2-placement of (p,q)-trees

Discussiones Mathematicae Graph Theory

Let G = (L,R;E) be a bipartite graph such that V(G) = L∪R, |L| = p and |R| = q. G is called (p,q)-tree if G is connected and |E(G)| = p+q-1. Let G = (L,R;E) and H = (L',R';E') be two (p,q)-tree. A bijection f:L ∪ R → L' ∪ R' is said to be a biplacement of G and H if f(L) = L' and f(x)f(y) ∉ E' for every edge xy of G. A biplacement of G and its copy is called 2-placement of G. A bipartite graph G is 2-placeable if G has a 2-placement. In this paper we give all (p,q)-trees which...

### A bijection between planar constellations and some colored Lagrangian trees.

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

### A bound for the Steiner tree problem in graphs

Mathematica Slovaca

Kybernetika

### A characterization of roman trees

Discussiones Mathematicae Graph Theory

A Roman dominating function (RDF) on a graph G = (V,E) is a function f: V → 0,1,2 satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of f is $w\left(f\right)={\sum }_{v\in V}f\left(v\right)$. The Roman domination number is the minimum weight of an RDF in G. It is known that for every graph G, the Roman domination number of G is bounded above by twice its domination number. Graphs which have Roman domination number equal to twice their domination number are called...

### A combinatorial derivation of the number of labeled forests.

Journal of Integer Sequences [electronic only]

### A combinatorial proof of Postnikov's identity and a generalized enumeration of labeled trees.

The Electronic Journal of Combinatorics [electronic only]

### A combinatorial ranking problem.

Aequationes mathematicae

### A combinatorial ranking problem. (Short Communication).

Aequationes mathematicae

### A Décomposition Theorem on Euclidean Steiner Minimal Trees.

Discrete &amp; computational geometry

### A distance between isomorphism classes of trees

Czechoslovak Mathematical Journal

### A few remarks on the history of MST-problem

Archivum Mathematicum

On the background of Borůvka’s pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.

### A formula for all minors of the adjacency matrix and an application

Special Matrices

We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.

### A generalization of Hamiltonian cycles for trees

Czechoslovak Mathematical Journal

### A Generalization of the Matrix-Tree Theorem.

Mathematische Zeitschrift

### A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs

Rendiconti del Seminario Matematico della Università di Padova

### A Link Between Ordered Sets And Trees On The Rectangle Tree Hypothesis

Publications de l'Institut Mathématique

### A lower bound for the irredundance number of trees

Discussiones Mathematicae Graph Theory

Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska  presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of Lemańska's result. ...

### A modification of the median of a tree

Mathematica Bohemica

The concept of median of a tree is modified, considering only distances from the terminal vertices instead of distances from all vertices.

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