one edge to another, a symmetric graph must also be edge-transitive. However, an edge-transitive graph need not be symmetric, since a—b might map to...
11 KB (1,158 words) - 12:55, 15 May 2023
graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive. In other words, a graph is...
5 KB (488 words) - 06:36, 5 June 2024
Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph, the Heawood graph and the...
6 KB (646 words) - 00:32, 8 October 2024
two edges are symmetric to each other, but some two vertices are not symmetric. Jon Folkman was inspired to define and research these graphs in a 1967 paper...
12 KB (1,392 words) - 05:03, 15 April 2024
The 110-vertex Iofinova–Ivanov graph is, in graph theory, a semi-symmetric cubic graph with 110 vertices and 165 edges. Iofinova and Ivanov proved in...
5 KB (534 words) - 00:39, 24 July 2024
is vertex-transitive and edge-transitive but not symmetric. A skew-symmetric graph is a directed graph together with a permutation σ on the vertices that...
14 KB (1,352 words) - 15:22, 1 August 2024
Therefore, the Ljubljana graph is a semi-symmetric graph, the third smallest possible cubic semi-symmetric graph after the Gray graph on 54 vertices and the...
5 KB (582 words) - 17:41, 30 August 2023
Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Holt graph Horton...
14 KB (1,251 words) - 14:50, 13 March 2024
Laplacian matrix (redirect from Kirchhoff matrix (of a graph))
\end{cases}}} The symmetrically normalized Laplacian matrix is symmetric if and only if the adjacency matrix is symmetric. For a non-symmetric adjacency matrix...
45 KB (5,041 words) - 22:13, 30 September 2024
Tutte 12-cage (category Individual graphs)
semi-symmetric graph on 126 vertices and is the fifth smallest possible cubic semi-symmetric graph after the Gray graph, the Iofinova–Ivanov graph on 110...
5 KB (616 words) - 19:49, 23 July 2024
the Gray graph is a semi-symmetric graph, the smallest possible cubic semi-symmetric graph. The characteristic polynomial of the Gray graph is ( x − 3...
7 KB (812 words) - 14:14, 28 April 2024
local edge-connectivity is symmetric. A graph is called k-edge-connected if its edge connectivity is k or greater. A graph is said to be maximally connected...
17 KB (2,062 words) - 20:41, 26 September 2024
In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for...
5 KB (543 words) - 19:54, 29 May 2021
vertex-transitive graphs are walk-regular. The semi-symmetric graphs are walk-regular.[unreliable source] The distance-regular graphs are walk-regular...
4 KB (613 words) - 14:49, 7 October 2024
groups of finite rank. In graph theory, he was the first to study semi-symmetric graphs, and he discovered the semi-symmetric graph with the fewest possible...
12 KB (1,126 words) - 19:50, 22 June 2024
Eulerian path (redirect from Semi-Eulerian graph)
and symmetric are guaranteed to be Eulerian. However, this is not a necessary condition, as it is possible to construct a non-symmetric, even graph that...
27 KB (3,269 words) - 00:33, 2 October 2024
graphs include the Gray graph (the smallest semi-symmetric cubic graph), the Ljubljana graph, and the Tutte 12-cage. The Frucht graph is one of the five smallest...
15 KB (1,777 words) - 20:46, 11 March 2024
colors), and either semi-symmetric or biregular. Examples of edge but not vertex transitive graphs include the complete bipartite graphs K m , n {\displaystyle...
5 KB (515 words) - 08:29, 18 August 2023
For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of...
46 KB (6,130 words) - 06:34, 24 May 2024
seems that the Dejter graph is the smallest symmetric graph having a connected self-complementary vertex-spanning semi-symmetric cubic subgraph. Both the...
4 KB (576 words) - 13:03, 29 August 2022
Logarithmic scale (redirect from Logarithmic graph paper)
2^5). Exponential growth curves are often depicted on a logarithmic scale graph. The markings on slide rules are arranged in a log scale for multiplying...
13 KB (1,206 words) - 10:43, 8 October 2024
The Folkman graph, a quartic graph with 20 vertices, the smallest semi-symmetric graph. The Meredith graph, a quartic graph with 70 vertices that is 4-connected...
6 KB (645 words) - 08:20, 12 October 2023
scientist Roy Folkman, an Israeli politician Folkman graph, a type of semi-symmetric graph in graph theory Folkman's theorem, a theorem in arithmetic combinatorics...
506 bytes (87 words) - 14:52, 20 September 2023
Dragan Marušič (category Graph theorists)
and half-transitive graphs. With co-authors, he proved that the Gray graph on 54 vertices is the smallest cubic semi-symmetric graph. He has well over 100...
10 KB (1,037 words) - 19:19, 2 October 2024
edges, and "semi-symmetric" means that every two edges are symmetric to each other but the same is not true for the vertices. This graph is the smallest...
8 KB (747 words) - 19:34, 9 July 2024
The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG...
7 KB (879 words) - 01:06, 4 April 2024
Carolina Araujo, Brazilian algebraic geometer Gabriela Araujo-Pardo, Mexican graph theorist, president of Mexican Mathematical Society Maria Angela Ardinghelli...
192 KB (22,835 words) - 23:38, 13 October 2024
graph is almost symmetric if its automorphism group has finitely many orbits. As he shows, for every connected locally finite almost-symmetric graph,...
21 KB (3,110 words) - 07:44, 15 October 2024
Hypergraph (redirect from Host graph)
describe properties of line-symmetric graphs. Note the obvious but important observation that every line-symmetric graph is line-regular. Karypis, G....
47 KB (6,211 words) - 13:39, 9 September 2024
Truncated icosahedron (redirect from Truncated icosahedral graph)
truncated icosahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces...
15 KB (1,531 words) - 06:16, 26 September 2024