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...

\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...

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

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...

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...

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...

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...

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...