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- Lutz Volkmann, Bohdan Zelinka
- Discrete Applied Mathematics
- 2005

- Bohdan Zelinka
- Discrete Mathematics
- 1996

- Bohdan Zelinka
- 2002

The signed edge domination number of a graph is an edge variant of the signed domination number. The closed neighbourhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end vertex with e. Let f be a mapping of the edge set E(G) of G into the set {−1, 1}. If ∑ x∈N [e] f(x) 1 for each e ∈ E(G), then f is called a… (More)

- Bohdan Zelinka
- Discussiones Mathematicae Graph Theory
- 1998

Two classes of graphs which are maximal with respect to the absence of Hamiltonian paths are presented. Block graphs with this property are characterized.

Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances .

- Bohdan Zelinka
- Discrete Mathematics
- 1990

A subset D of the vertex set V (G) of a graph G is called point-set dominating, if for each subset S ⊆ V (G) − D there exists a vertex v ∈ D such that the subgraph of G induced by S ∪ {v} is connected. The maximum number of classes of a partition of V (G), all of whose classes are point-set dominating sets, is the point-set domatic number dp(G) of G. Its… (More)

The paper studies the domatic numbers and the total domatic numbers of graphs having cut-vertices. We shall study the domatic number d(G) and the total domatic number d t (G) of a graph G. A survey of the related theory is given in 3]. We consider nite, undirected graphs without loops or multiple edges. A subset D of the vertex set V (G) of a graph G is… (More)

- Bohdan Zelinka
- Kybernetika
- 1973

- Ivan Havel, Bohdan Zelinka
- Discussiones Mathematicae Graph Theory
- 2001

We deal with the graph operator Pow2 defined to be the complement of the square of a graph: Pow2(G) = Pow2(G). Motivated by one of many open problems formulated in [6] we look for graphs that are 2-periodic with respect to this operator. We describe a class G of bipartite graphs possessing the above mentioned property and prove that for any m,n ≥ 6, the… (More)