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...

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

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...

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...

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...

Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference is equivalent...