In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving...

of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is...

nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any...

v 2 . {\displaystyle f(v_{1})=v_{2}.} In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices...

a mapping of a graph onto itself, i.e., when G and H are one and the same graph, the isomorphism is called an automorphism of G. Graph isomorphism is...

mathematical field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism of G that maps...

"field automorphisms" (generated by a Frobenius automorphism), and g is the order of the group of "graph automorphisms" (coming from automorphisms of the...

construction as a Kneser graph. The Petersen graph is a core: every homomorphism of the Petersen graph to itself is an automorphism. As shown in the figures...

neighborhood of any vertex in the Gosset graph is isomorphic to the Schläfli graph. The automorphism group of the Gosset graph is isomorphic to the Coxeter group...

problems. Finding a graph's automorphism group. Counting automorphisms of a graph. The recognition of self-complementarity of a graph or digraph. A clique...

{\displaystyle \sigma :V(\Gamma )\to V(\Gamma )} be an arbitrary automorphism of the colored directed graph Γ {\displaystyle \Gamma } , and let h = σ ( e ) {\displaystyle...

alternating path; see alternating. automorphism A graph automorphism is a symmetry of a graph, an isomorphism from the graph to itself. bag One of the sets...

In mathematics, the outer automorphism group of a group, G, is the quotient, Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is...

graphs with large automorphism groups: vertex-transitive, arc-transitive, and distance-transitive graphs; strongly regular graphs and their generalizations...

degree 22. Thus all 100 vertices have degree 22 each. The automorphism group of the Higman–Sims graph is a group of order 88,704,000 isomorphic to the semidirect...

Hoffman-Singleton graph. It should instead be ( − 1 ) a b y {\displaystyle (-1)^{a}by} as written here.) The automorphism group of the Hoffman–Singleton graph is a...

The automorphism group of the Shrikhande graph is of order 192. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore...

second branch of algebraic graph theory involves the study of graphs in connection to group theory, particularly automorphism groups and geometric group...

and no vertex embedded into a point within an edge. The automorphism group of the Heawood graph is isomorphic to the projective linear group PGL2(7), a...

polynomial, making it a graph determined by its spectrum. The 5-regular Clebsch graph is a Cayley graph with an automorphism group of order 1920, isomorphic...

Brouwer–Haemers graph Local McLaughlin graph Perkel graph Gewirtz graph A symmetric graph is one in which there is a symmetry (graph automorphism) taking any...

same number of vertices. The Wagner graph is a vertex-transitive graph but is not edge-transitive. Its full automorphism group is isomorphic to the dihedral...

the five smallest cubic graphs without any symmetries: it possesses only a single graph automorphism, the identity automorphism. According to Brooks' theorem...

mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that...

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

distance-transitive graph is interesting partly because it has a large automorphism group. Some interesting finite groups are the automorphism groups of distance-transitive...

possessing only a single graph automorphism, the identity: every vertex can be distinguished topologically from every other vertex. Such graphs are called asymmetric...

to five edges in the Tutte–Coxeter graph is equivalent to any other such path by one such automorphism. This graph is the spherical building associated...

identity mapping of a graph is always an automorphism, and is called the trivial automorphism of the graph. An asymmetric graph is a graph for which there are...

be extended to an automorphism of the whole graph. A rook's graph can also be viewed as the line graph of a complete bipartite graph Kn,m — that is, it...