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...

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...

Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph, the Heawood graph and the...

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...

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...

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...

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

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...

\end{cases}}} The symmetrically normalized Laplacian matrix is symmetric if and only if the adjacency matrix is symmetric. For a non-symmetric adjacency matrix...

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...

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...

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...

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...

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...

colors), and either semi-symmetric or biregular. Examples of edge but not vertex transitive graphs include the complete bipartite graphs K m , n {\displaystyle...

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...

from expanding too rapidly and becoming too large to fit within a small graph. The markings on slide rules are arranged in a log scale for multiplying...

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...

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...

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...

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...

seems that the Dejter graph is the smallest symmetric graph having a connected self-complementary vertex-spanning semi-symmetric cubic subgraph. Both the...

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...

describe properties of line-symmetric graphs. Note the obvious but important observation that every line-symmetric graph is line-regular. Karypis, G....

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...

vertex-transitive graphs are walk-regular. The semi-symmetric graphs are walk-regular.[unreliable source] The distance-regular graphs are walk-regular...

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...

Carolina Araujo, Brazilian algebraic geometer Gabriela Araujo-Pardo, Mexican graph theorist, president of Mexican Mathematical Society Maria Angela Ardinghelli...

truncated dodecahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces...

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...