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...

In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by...

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...

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

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

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...

the OEIS) Edge-transitive graphs include all symmetric graph, such as the vertices and edges of the cube. Symmetric graphs are also vertex-transitive...

real skew-symmetric matrices with graph G {\displaystyle G} have at most 2 k {\displaystyle 2k} nonzero eigenvalues. Note that the (simple) graph of a real...

to be symmetric ( S = S − 1 {\displaystyle S=S^{-1}} ) and not containing the group identity element. In this case, the uncolored Cayley graph can be...

other automorphisms. Note that the term "asymmetric graph" is not a negation of the term "symmetric graph," as the latter refers to a stronger condition than...

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...

families of graphs based on symmetry (such as symmetric graphs, vertex-transitive graphs, edge-transitive graphs, distance-transitive graphs, distance-regular...

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...

vertices, on the edges and on the arcs of the graph. Therefore, the Heawood graph is a symmetric graph. It has automorphisms that take any vertex to any...

maximum size of the graph is ⁠n(n − 1)/2⁠. The edges of an undirected simple graph permitting loops G {\displaystyle G} induce a symmetric homogeneous relation...

called loop-digraphs (see section Types of directed graph). Symmetric directed graphs are directed graphs where all edges appear twice, one in each direction...

In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August...

skew-symmetric graph is the double covering graph of a bidirected graph. A bidirected graph may be regarded as an orientation of a signed graph, similarly...

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

the Petersen graph has non-orientable genus 1. The Petersen graph is strongly regular (with signature srg(10,3,0,1)). It is also symmetric, meaning that...

matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory....

In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David...

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

or skew-symmetric may refer to: Antisymmetry in linguistics Antisymmetry in physics Antisymmetric relation in mathematics Skew-symmetric graph Self-complementary...

individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the...

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique...

n-cycle is a symmetric graph. Similarly to the Platonic graphs, the cycle graphs form the skeletons of the dihedra. Their duals are the dipole graphs, which...

Desargues graph is one of only seven symmetric Generalized Petersen graphs. Among these seven graphs are the cubical graph G(4, 1), the Petersen graph G(5,...

two sides of its bipartition are not symmetric with each other, making it the smallest possible semi-symmetric graph. It is named after Jon Folkman, who...

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...