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UML class diagram of a Graph (abstract data type) The basic operations provided by a graph data structure G usually include: [1] adjacent(G, x, y): tests whether there is an edge from the vertex x to the vertex y; neighbors(G, x): lists all vertices y such that there is an edge from the vertex x to the vertex y;
A class diagram exemplifying the singleton pattern. In object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance. It is one of the well-known "Gang of Four" design patterns, which describe how to solve recurring problems in object-oriented software. [1]
An object graph is a view of an object system at a particular point in time. Unlike a normal data model such as a Unified Modeling Language (UML) class diagram, which details the relationships between classes, the object graph relates their instances. Object diagrams are subsets of the overall object graph.
Additional examples include the following special cases: In an empty graph, each vertex forms a component with one vertex and zero edges. [3] More generally, a component of this type is formed for every isolated vertex in any graph. [4] In a connected graph, there is exactly one component: the whole graph. [4] In a forest, every component is a ...
The edge-connectivity for a graph with at least 2 vertices is less than or equal to the minimum degree of the graph because removing all the edges that are incident to a vertex of minimum degree will disconnect that vertex from the rest of the graph. [1] For a vertex-transitive graph of degree d, we have: 2(d + 1)/3 ≤ κ(G) ≤ λ(G) = d. [11]
A different method uses an inductive construction of 3-connected graphs to incrementally build planar embeddings of every 3-connected component of G (and hence a planar embedding of G itself). [19] The construction starts with K 4 and is defined in such a way that every intermediate graph on the way to the full component is again 3-connected ...
LEMON has its own graph storing format, the so called Lemon Graph Format and includes general EPS drawing methods and special graph exporting tools. LEMON also includes several miscellaneous tools. For example, it provides simple tools for measuring the performance of algorithms, which can be used to compare different implementations of the ...
The Turán graph T(13,4), an example of a cograph. In graph theory, a cograph, or complement-reducible graph, or P 4-free graph, is a graph that can be generated from the single-vertex graph K 1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K 1 and is closed under ...