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...

the Moore graphs are sometimes defined as including the graphs that exactly meet this bound. Again, any such graph must be a cage. The Hoffman–Singleton...

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

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...

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...

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

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

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 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...

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

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...

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...

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...

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

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...

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

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

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

employment-oriented social network. It was launched on May 5, 2003 by Reid Hoffman and Eric Ly. Since December 2016, LinkedIn has been a wholly owned subsidiary...

In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph...