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...

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

graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism f...

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...

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...

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

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

{\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...

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

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

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...

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...

Graph automorphism Graph coloring Graph database Graph data structure Graph drawing Graph equation Graph rewriting Graph sandwich problem Graph property...

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...

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...

up to an element of S6 (an inner automorphism)) yields an outer automorphism S6 → S6. This map is an outer automorphism, since a transposition does not...

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...

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...

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...

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...

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...

distance-transitive graphs, having the numerical regularity properties of the latter without necessarily having a large automorphism group. The intersection...

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

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...

of the Hall-Janko group as an index 2 subgroup of its automorphism group. The Hall–Janko graph can be constructed out of objects in U3(3), the simple...

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...

The automorphism group of a graph is the automorphism group of its complement. The complement of every triangle-free graph is a claw-free graph, although...

star has large automorphism group, namely, the symmetric group on k letters. Stars may also be described as the only connected graphs in which at most...

k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended to an automorphism of the...

mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices...