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...
24 KB (2,926 words) - 19:05, 30 April 2024
They include the Petersen graph and generalize one of the ways of constructing the Petersen graph. The generalized Petersen graph family was introduced...
13 KB (1,395 words) - 05:18, 25 May 2024
The Petersen Graph is a mathematics book about the Petersen graph and its applications in graph theory. It was written by Derek Holton and John Sheehan...
5 KB (616 words) - 20:31, 19 February 2024
matrix of a graph (this part of algebraic graph theory is also called spectral graph theory). For the Petersen graph, for example, the spectrum of the adjacency...
7 KB (671 words) - 16:56, 27 November 2023
snark is planar. The first graph known to be a snark was the Petersen graph; it was proved to be a snark by Julius Petersen in 1898, although it had already...
23 KB (2,707 words) - 07:38, 22 July 2024
databases. The name "Desargues graph" has also been used to refer to a ten-vertex graph, the complement of the Petersen graph, which can also be formed as...
10 KB (1,203 words) - 11:19, 3 August 2024
graph Cameron graph Petersen graph Hall–Janko graph Hoffman–Singleton graph Higman–Sims graph Paley graph of order 13 Shrikhande graph Schläfli graph...
14 KB (1,251 words) - 14:50, 13 March 2024
and these graphs are not 1-factorable; examples of such graphs include: Any regular graph with an odd number of nodes. The Petersen graph. A 1-factorization...
11 KB (1,237 words) - 08:22, 17 July 2024
Linkless embedding (redirect from Linklessly embeddable graph)
The complete graph K6, the Petersen graph, and the other five graphs in the Petersen family do not have linkless embeddings. Every graph minor of a linklessly...
29 KB (3,469 words) - 20:06, 19 February 2024
individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the...
15 KB (1,777 words) - 20:46, 11 March 2024
5 (section Graphs theory, and planar geometry)
number of 5. The Petersen graph, which is also a distance-regular graph, is one of only 5 known connected vertex-transitive graphs with no Hamiltonian...
87 KB (10,662 words) - 20:29, 8 August 2024
contributions to the field of mathematics led to the birth of graph theory. Petersen's interests in mathematics were manifold, including: geometry, complex...
11 KB (1,478 words) - 17:11, 21 June 2024
generalized Petersen graph G(9,2) is non-planar, triangle-free, and uniquely 3-edge-colorable. For many years it was the only known such graph, and it had...
10 KB (1,031 words) - 05:57, 3 May 2023
Ferdinand Möbius and Seligmann Kantor. It can be defined as the generalized Petersen graph G(8,3): that is, it is formed by the vertices of an octagon, connected...
13 KB (1,526 words) - 00:41, 24 July 2024
Heawood graph, the complete graph K7 (and hence K5 and K6), the Petersen graph (and hence the complete bipartite graph K3,3, since the Petersen graph contains...
7 KB (693 words) - 09:03, 29 November 2023
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...
35 KB (4,471 words) - 04:49, 30 April 2024
graph is a forest. More advanced kinds of graphs are: Petersen graph and its generalizations; perfect graphs; cographs; chordal graphs; other graphs with...
28 KB (3,689 words) - 23:54, 26 July 2024
9, −5]4. The Nauru graph can also be constructed as the generalized Petersen graph G(12, 5) which is formed by the vertices of a dodecagon connected to...
11 KB (1,378 words) - 16:58, 11 December 2023
Hemi-dodecahedron (section Petersen graph)
of graph theory this is an embedding of the Petersen graph on a real projective plane. With this embedding, the dual graph is K6 (the complete graph with...
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graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic solids). The finite Cayley graphs (such as cube-connected...
6 KB (636 words) - 07:48, 8 August 2024
O3 = K(5, 2) is the Petersen graph (see top right figure). The Kneser graph O4 = K(7, 3), visualized on the right. The Kneser graph K ( n , k ) {\displaystyle...
14 KB (1,626 words) - 12:35, 14 June 2024
graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...
67 KB (7,996 words) - 01:58, 29 July 2024
distance graphs include the cactus graphs, the matchstick graphs and penny graphs, and the hypercube graphs. The generalized Petersen graphs are non-strict...
33 KB (4,019 words) - 07:43, 18 July 2024
of graph theory, the odd graphs are a family of symmetric graphs defined from certain set systems. They include and generalize the Petersen graph. The...
15 KB (1,924 words) - 01:46, 29 November 2023
mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated...
13 KB (1,448 words) - 15:50, 4 June 2024
Edge coloring (category Graph coloring)
out" to referee the game). The case that n = 3 gives the well-known Petersen graph. As Biggs (1972) explains the problem (for n = 6), the players wish...
65 KB (8,472 words) - 07:37, 16 July 2024
Good Pub Guide, recommends pubs in the UK Generalized Petersen graph, a type of mathematical graph Guinness Peat Group, an investment holding company Grammophon-Philips...
701 bytes (118 words) - 14:49, 11 March 2020
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...
106 KB (15,667 words) - 12:01, 16 May 2024
hypohamiltonian graphs with at most 17 vertices is known: they are the 10-vertex Petersen graph, a 13-vertex graph and a 15-vertex graph found by computer...
24 KB (2,467 words) - 16:54, 28 November 2023
10-cage, the Harries graph and the Harries–Wong graph. The Petersen graph has a girth of 5 The Heawood graph has a girth of 6 The McGee graph has a girth of...
7 KB (903 words) - 09:27, 5 June 2024