mathematical field of graph theory, the Hoffman graph is a 4-regular graph with 16 vertices and 32 edges discovered by Alan Hoffman. Published in 1963,...

of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with...

graph. Moore graphs were named by Hoffman & Singleton (1960) after Edward F. Moore, who posed the question of describing and classifying these graphs...

two in the group of automorphisms of the Hoffman–Singleton graph. Take the M22 graph, a strongly regular graph srg(77,16,0,4) and augment it with 22 new...

Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Holt graph Horton...

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

graph on GQ(2, 4). The Hoffman–Singleton graph is an srg(50, 7, 0, 1). The Gewirtz graph is an srg(56, 10, 0, 2). The M22 graph aka the Mesner graph is...

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

Nauru graph and the Desargues graph are integral. The Higman–Sims graph, the Hall–Janko graph, the Clebsch graph, the Hoffman–Singleton graph, the Shrikhande...

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

6-cycles. The Coxeter graph may be derived from the Hoffman-Singleton graph. Take any vertex v in the Hoffman-Singleton graph. There is an independent...

of graphs. Hoffman and Robert Singleton constructed the Hoffman–Singleton graph, which is the unique Moore graph of degree 7 and diameter 2. Hoffman died...

Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability...

Auren Raphael Hoffman (born 1974) is an American entrepreneur, angel investor, author and CEO of SafeGraph, a firm that gathers location data from mobile...

intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring...

regular graphs, originally due to Alan J. Hoffman and Philippe Delsarte. Suppose that G {\displaystyle G} is a k {\displaystyle k} -regular graph on n {\displaystyle...

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...

various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)...

as generalizing symmetric graphs, that is, graphs that are both vertex- and edge-transitive. For example, the Hoffman graph is 1-walk-regular but not...

graph also occurs many times as an induced subgraph of the Hoffman–Singleton graph. Each of these instances is in fact an eigenvector of the Hoffman-Singleton...

It is a subgraph of the Hoffman–Singleton graph. Brouwer, A. E.; Cohen, A. M.; Neumaier, A. (1989), Distance-regular graphs, Springer-Verlag, Theorem...

Petersen graph (degree three), and the Hoffman–Singleton graph (degree seven). Only one more of these Moore graphs can exist, with degree 57. For all other...

(2012). The Hoffman–Singleton graph. Graph found by Sampels (1997). Graph found by Dinneen & Hafner (1994). Graphs found by Storwick (1970). Graph found by...

Man Who Loved Only Numbers, public lecture by Paul Hoffman "Open problems of Paul Erdős in graph theory" by Fan Chung Portals: Biography Hungary Mathematics...

of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which...

In 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...

200 countries and territories. It was launched on May 5, 2003 by Reid Hoffman and Eric Ly, receiving financing from numerous venture capital firms, including...

proven in Schrijver (1998). 6. Hoffman and Kruskal proved the following theorem. Suppose G {\displaystyle G} is a directed graph without 2-dicycles, P {\displaystyle...

bound; for 1 < k and 2 < d, only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs (not yet proven to exist) of diameter k = 2 and...

Hoffman–Singleton graph. Despite additional research on the properties such a graph must have, it is not known whether there are more of these graphs...