Graphs and Finite Permutation Groups.
Graphs and Finite Permutation Groups. II.
Graphs and quasitrivial groupoids
Graphs and their spectra
Graphs associated with codes of covering radius 1 and minimum distance 2.
Graphs associated with nilpotent Lie algebras of maximal rank.
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph...
Graphs determined by their (signless) Laplacian spectra.
Graphs for n-circular matroids
We give "if and only if" characterization of graphs with the following property: given n ≥ 3, edges of such graphs form matroids with circuits from the collection of all graphs with n fundamental cycles. In this way we refer to the notion of matroidal family defined by Simões-Pereira [2].
Graphs from Projective Planes.
Graphs having no quantum symmetry
We consider circulant graphs having vertices, with prime. To any such graph we associate a certain number , that we call type of the graph. We prove that for the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.
Graphs having planar complementary line (total) graphs.
Graphs in which each pair of vertices has exactly two common neighbours
The paper studies graphs in which each pair of vertices has exactly two common neighbours. It disproves a conjectury by P. Hliněný concerning these graphs.
Graphs in which Every Finite Path is Contained in a Circuit.
Graphs in which every path is contained in a Hamilton path.
Graphs isomorphic to their path graphs
We prove that for every number , the -iterated -path graph of is isomorphic to if and only if is a collection of cycles, each of length at least 4. Hence, is isomorphic to if and only if is a collection of cycles, each of length at least 4. Moreover, for we reduce the problem of characterizing graphs such that to graphs without cycles of length exceeding .
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.
Graphs maximal with respect to hom-properties
For a simple graph H, →H denotes the class of all graphs that admit homomorphisms to H (such classes of graphs are called hom-properties). We investigate hom-properties from the point of view of the lattice of hereditary properties. In particular, we are interested in characterization of maximal graphs belonging to →H. We also provide a description of graphs maximal with respect to reducible hom-properties and determine the maximum number of edges of graphs belonging to →H.
Graphs minimal with respect to contractions in some subfamilies of maximal planar graphs
Graphs of actions on R-trees.
Graphs of diameter 2 with cyclic defect