Graph invariants and large cycles: a survey.
Graph pattern analysis with PatternGravisto.
Graphes de Ramanujan et applications
Graphes maximaux
Graphs and their 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 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 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 which are edge-locally
Graphs which are locally paths
Graphs whose energy does not exceed 3
Graphs whose minimal rank is two.
Graphs whose minimal rank is two: the finite fields case.
Graphs with 3-Rainbow Index n − 1 and n − 2
Let G = (V (G),E(G)) be a nontrivial connected graph of order n with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ N, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree connecting S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for each k-subset S of V (G) is called the k-rainbow index of G, denoted by...
Graphs with 4-Rainbow Index 3 and n − 1
Let G be a nontrivial connected graph with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ ℕ, where adjacent edges may be colored the same. A tree T in G is called a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree that connects S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for every set S of k vertices of V (G) is called the k-rainbow index of G, denoted by rxk(G)....
Graphs with a given edge neighbourhood
Graphs with four boundary vertices.
Graphs with given degree sequence and maximal spectral radius.