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
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) - 04:07, 23 August 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 (632 words) - 23:28, 12 August 2024
the OEIS) Edge-transitive graphs include all symmetric graph, such as the vertices and edges of the cube. Symmetric graphs are also vertex-transitive...
5 KB (515 words) - 08:29, 18 August 2023
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...
29 KB (4,690 words) - 21:09, 11 May 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
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...
10 KB (1,001 words) - 13:25, 14 August 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) - 09:56, 10 July 2024
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...
17 KB (2,318 words) - 08:39, 16 July 2024
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...
23 KB (2,938 words) - 07:47, 18 July 2024