Antidomatic number of a graph.
A note on periodicity of the 2-distance operator
The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class of all finite undirected graphs. If G is a graph from , then T₂(G) is the graph with the same vertex set as G in which two vertices are adjacent if and only if their distance in G is 2. E. Prisner asks whether the periodicity ≥ 3 is possible for T₂. In this paper an affirmative answer is given. A result concerning the periodicity 2 is added.
Graphs maximal with respect to absence of hamiltonian paths
Two classes of graphs which are maximal with respect to the absence of Hamiltonian paths are presented. Block graphs with this property are characterized.
On the simplex graph operator
A simplex of a graph G is a subgraph of G which is a complete graph. The simplex graph Simp(G) of G is the graph whose vertex set is the set of all simplices of G and in which two vertices are adjacent if and only if they have a non-empty intersection. The simplex graph operator is the operator which to every graph G assigns its simplex graph Simp(G). The paper studies graphs which are fixed in this operator and gives a partial answer to a problem suggested by E. Prisner.
Vztah díla E. C. Hammersteina k časopisu Pokroky matematiky, fyziky a astronomie
Nad jednou starou knihou
Homogeneous digraphs
The group of autotopies of a digraph
Centrally symmetric Hasse diagrams of finite modular lattices
Isotopy of digraphs
Groups and homogeneous graphs
Tolerance in algebraic structures
Intersection graphs of finite abelian groups
Graph representations of finite Abelian groups
On a problem of P. Vestergaard concerning circuits in graphs
Tolerances on graph algebras
Embedding trees into block graphs
A remark on systems of maximal cliques of a graph
Tolerance relations on periodic commutative semigroups
Tolerances and congruences on tree algebras
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