Does a Moore graph with girth 5 and degree 57 exist? (more unsolved problems in mathematics) In graph theory, a Moore graph is a regular graph whose girth...

mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful...

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...

nonplanar graph contains either K3,3 or the complete graph K5 as a minor; this is Wagner's theorem. Every complete bipartite graph. Kn,n is a Moore graph and...

regular graphs with a given degree and number of vertices. Random regular graph Strongly regular graph Moore graph Cage graph Highly irregular graph Chen...

extended Moore neighbourhood of range r is (2r + 1)2. The idea behind the formulation of Moore neighborhood is to find the contour of a given graph. This...

while trying to classify all Moore graphs, and is the highest-order Moore graph known to exist. Since it is a Moore graph where each vertex has degree...

unique smallest cubic graph of girth 8, it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle...

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...

known that an (r, g)-graph exists for any combination of r ≥ 2 and g ≥ 3. It follows that all (r, g)-cages exist. If a Moore graph exists with degree r...