mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain...

concerned with enumerating in this sense. For instance, in partition enumeration and graph enumeration the objective is to count partitions or graphs that meet...

to many counting problems, in particular to the enumeration of chemical compounds. The Pólya enumeration theorem has been incorporated into symbolic combinatorics...

symmetries that map any vertex to any other vertex. In the context of graph enumeration and graph isomorphism it is important to distinguish between labeled vertices...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

graphs representing the same partial order have the same set of topological orders. The graph enumeration problem of counting directed acyclic graphs...

finding or estimating the number of graphs with a given degree sequence is a problem from the field of graph enumeration. More generally, the degree sequence...

known as the vertex enumeration problem and the problem of the construction of a H-representation is known as the facet enumeration problem. While the...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

bijective. Therefore, the same sequence of numbers also solves the graph enumeration problem for complete digraphs. There is an explicit but complicated...

the goal of constructions, like the enumeration of all graphs from some starting graph, i.e. the generation of a graph language – instead of simply transforming...

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain...

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect...

" Harary's work in graph theory was diverse. Some topics of great interest to him were: Graph enumeration, that is, counting graphs of a specified kind...

In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In...

graph of f, that is, the set of all pairs ⟨ x , f ( x ) ⟩ {\displaystyle \langle x,f(x)\rangle } such that f(x) is defined, is computably enumerable....

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

These numbers can be used to solve several problems in combinatorial enumeration. The nth number in the sequence (starting with the number 0 for n = 0)...

In graph theory, a tree is an undirected graph in which every pair of distinct vertices is connected by exactly one path, or equivalently, a connected...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

specializing in combinatorics, including graph enumeration and the topological properties of random graphs. She is a professor in the Institute of Discrete...

it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism...

the largest k for which the graph is k-edge-connected. Edge connectivity and the enumeration of k-edge-connected graphs was studied by Camille Jordan...

general. Graphs are fundamental objects in combinatorics. Considerations of graph theory range from enumeration (e.g., the number of graphs on n vertices...

terms of graph theory, by considering it in terms of constructing a graph coloring of the planar graph of adjacencies between regions. In graph-theoretic...

distance 2 of a central path. Caterpillars provide one of the rare graph enumeration problems for which a precise formula can be given: when n ≥ 3, the...

free dictionary. Unlabeled coloring, in graph theory Graph enumeration § Labeled vs unlabeled problems Tree (graph theory) § Unlabeled trees Unlabeled sexuality...

In graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating...

pp. 321–324. Schwenk, Allen J. (1989), "Enumeration of Hamiltonian cycles in certain generalized Petersen graphs", Journal of Combinatorial Theory, Series...

In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0...