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In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations...

the whole graph. Components are sometimes called connected components. The number of components in a given graph is an important graph invariant, and is...

induced subgraph of a graph G for vertex subset S. Prime symbol ' The prime symbol is often used to modify notation for graph invariants so that it applies...

labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined...

the two forbidden minors K4 and K2,3, or by their Colin de Verdière graph invariants. They have Hamiltonian cycles if and only if they are biconnected,...

} // computed invariant: ICount % 3 == 1 || ICount % 3 == 2 } Erlangen program Graph invariant Invariant differential operator Invariant estimator in statistics...

Colin de Verdière's invariant is a graph parameter μ ( G ) {\displaystyle \mu (G)} for any graph G, introduced by Yves Colin de Verdière in 1990. It was...

additional face while keeping the graph planar would keep v – e + f an invariant. Since the property holds for all graphs with f = 2, by mathematical induction...

algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants. The first branch of algebraic graph theory...

graph is the non-increasing sequence of its vertex degrees; for the above graph it is (5, 3, 3, 2, 2, 1, 0). The degree sequence is a graph invariant...

is a graph parameter mr ⁡ ( G ) {\displaystyle \operatorname {mr} (G)} for a graph G. It was motivated by the Colin de Verdière graph invariant. The adjacency...

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed...

valid e-graph conforms to several data structure invariants. Two e-nodes are equivalent if they are in the same e-class. The congruence invariant states...

genus in this sense since it is not invariant concerning cobordisms. Genus can be also calculated for the graph spanned by the net of chemical interactions...

Colin de Verdière graph invariant μ = 6 {\displaystyle \mu =6} . The K 7 {\displaystyle K_{7}} -family is generated from the complete graph K 7 {\displaystyle...

The Heawood graph is the smallest cubic graph with Colin de Verdière graph invariant μ = 6. The Heawood graph is a unit distance graph: it can be embedded...

In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring...

a graph polynomial is a graph invariant whose value is a polynomial. Invariants of this type are studied in algebraic graph theory. Important graph polynomials...

In graph theory, boxicity is a graph invariant, introduced by Fred S. Roberts in 1969. The boxicity of a graph is the minimum dimension in which a given...

mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful...