Rook's graphIn graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and there is an edge between any two squares sharing a row (rank) or column (file), the squares that a rook can move between. These graphs can be constructed for chessboards of any rectangular shape.
Partition en cliquesEn théorie des graphes, une couverture par cliques ou une partition en cliques d'un graphe non orienté est une partition des sommets du graphe en cliques, c'est-à-dire en des ensembles de sommets à l'intérieur desquels deux sommets sont adjacents. Un couverture par cliques minimale est une couverture de taille minimale, c'est-à-dire par un nombre minimal de cliques. Le problème de la couverture par cliques est le problème algorithmique qui consiste à trouver une couverture par cliques minimale.
Graphe moulinEn théorie des graphes, le graphe moulin Wd(k,n) est un graphe non orienté construit, pour deux entiers k ≥ 2 et n ≥ 2, en joignant n copies du graphe complet Kk à un sommet universel partagé. Autrement dit, il s'agit d'une somme, sur une clique à 1 seul sommet, de ces n graphes complets. Le graphe moulin Wd(k,n) a (k−1) n + 1 sommets et nk (k − 1) / 2 arêtes, il est de maille 3 (pour k > 2), de rayon 1 et de diamètre 2.
Lovász numberIn graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász theta function and is commonly denoted by , using a script form of the Greek letter theta to contrast with the upright theta used for Shannon capacity. This quantity was first introduced by László Lovász in his 1979 paper On the Shannon Capacity of a Graph. Accurate numerical approximations to this number can be computed in polynomial time by semidefinite programming and the ellipsoid method.
K-arbrevignette|Le graphe de Goldner–Harary est un exemple d'un 3-arbre planaire. En théorie des graphes, un k- arbre est un type de graphe non orienté. Un graphe est un k-arbre s'il peut être obtenu de la manière suivante : on part du graphe complet à ( k + 1) sommets, puis on ajoute des sommets tels que, pour un sommet v ajouté, v a exactement k voisins dans le graphe au moment de l'ajout, et ces voisins forment une clique. Les k-arbres sont exactement les graphes de largeur arborescente donnée, maximaux au sens que l'on ne peut pas ajouter d'arêtes sans augmenter leur largeur arborescente.
Parity graphIn graph theory, a parity graph is a graph in which every two induced paths between the same two vertices have the same parity: either both paths have odd length, or both have even length. This class of graphs was named and first studied by . Parity graphs include the distance-hereditary graphs, in which every two induced paths between the same two vertices have the same length.
Modular graphIn graph theory, a branch of mathematics, the modular graphs are undirected graphs in which every three vertices x, y, and z have at least one median vertex m(x, y, z) that belongs to shortest paths between each pair of x, y, and z. Their name comes from the fact that a finite lattice is a modular lattice if and only if its Hasse diagram is a modular graph. It is not possible for a modular graph to contain a cycle of odd length. For, if C is a shortest odd cycle in a graph, x is a vertex of C, and yz is the edge of C farthest from x, there could be no median m(x, y, z).
Line perfect graphIn graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple cycle is a triangle. A graph is line perfect if and only if each of its biconnected components is a bipartite graph, the complete graph K_4, or a triangular book K_1,1,n. Because these three types of biconnected component are all perfect graphs themselves, every line perfect graph is itself perfect.
Disjoint union of graphsIn graph theory, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is analogous to the disjoint union of sets, and is constructed by making the vertex set of the result be the disjoint union of the vertex sets of the given graphs, and by making the edge set of the result be the disjoint union of the edge sets of the given graphs. Any disjoint union of two or more nonempty graphs is necessarily disconnected.
Biconnected componentIn graph theory, a biconnected component (sometimes known as a 2-connected component) is a maximal biconnected subgraph. Any connected graph decomposes into a tree of biconnected components called the block-cut tree of the graph. The blocks are attached to each other at shared vertices called cut vertices or separating vertices or articulation points. Specifically, a cut vertex is any vertex whose removal increases the number of connected components.
