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...

itself, i.e., when G and H are one and the same graph, the bijection is called an automorphism of G. If a graph is finite, we can prove it to be bijective...

computationally equivalent to the problem of computing the automorphism group of a graph, and is weaker than the permutation group isomorphism problem...

mathematical field of graph theory, a vertex-transitive graph is a graph G in which, given any two vertices v1 and v2 of G, there is some automorphism f : V ( G )...

{\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...

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

"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...

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...

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...

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...

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

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...

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

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...

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...

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...

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...

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

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...

cyclic graph, but this term has other meanings. Circulant graphs can be described in several equivalent ways: The automorphism group of the graph includes...

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...

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...

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...

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...

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...