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A t-transitive graph is a graph such that the automorphism group acts transitively on t-arcs, but not on (t + 1)-arcs. Since 1-arcs are simply edges, every symmetric graph of degree 3 or more must be t -transitive for some t , and the value of t can be used to further classify symmetric graphs.
Each Johnson graph is locally grid, meaning that the induced subgraph of the neighbors of any vertex is a rook's graph. More precisely, in the Johnson graph J ( n , k ) {\displaystyle J(n,k)} , each neighborhood is a k × ( n − k ) {\displaystyle k\times (n-k)} rook's graph.
A "harmonious labeling" on a graph G is an injection from the vertices of G to the group of integers modulo k, where k is the number of edges of G, that induces a bijection between the edges of G and the numbers modulo k by taking the edge label for an edge (x, y) to be the sum of the labels of the two vertices x, y (mod k). A "harmonious graph ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
This second branch of algebraic graph theory is related to the first, since the symmetry properties of a graph are reflected in its spectrum. In particular, the spectrum of a highly symmetrical graph, such as the Petersen graph, has few distinct values [ 1 ] (the Petersen graph has 3, which is the minimum possible, given its diameter).
The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...
In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer. [1] [2] It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. It has chromatic number 3, diameter 3, and is 5-vertex ...
The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,.. In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices , with predicates for equality and adjacency testing.