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Graph. [] A graph with three vertices and three edges. In one restricted but very common sense of the term, [ 1 ][ 2 ] a graph is an ordered pair comprising: V {\displaystyle V} , a set of vertices (also called nodes or points); E ⊆ {{x, y} ∣ x, y ∈ V and x ≠ y} {\displaystyle E\subseteq \ {\ {x,y\}\mid x,y\in V\; {\textrm {and}}\;x\neq ...
In graph theory, an n -dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols. It has mn vertices, consisting of all possible length-n sequences of the given symbols; the same symbol may appear multiple times in a sequence. For a set of m symbols S = {s1, …, sm}, the set of vertices is:
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2. Feedback vertex set [2][3]: GT7. Feedback arc set [2][3]: GT8.
Axiom is a general-purpose computer algebra system. It has been in development since 1971 by IBM, and was originally named scratchpad. Richard Jenks originally headed it but over the years Barry Trager who then shaped the direction of the scratchpad project took over the project. It was eventually sold to the Numerical Algorithms Group (NAG ...
A simple graph contains no double edges or loops. [1] The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. [2] If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special ...
Greedy coloring. Two greedy colorings of the same crown graph using different vertex orders. The right example generalises to 2-colorable graphs with n vertices, where the greedy algorithm expends n/2 colors. In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring[1] is a coloring of ...
A graph with six vertices and seven edges. In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices ...
In graph theory, a deletion-contraction formula / recursion is any formula of the following recursive form: Here G is a graph, f is a function on graphs, e is any edge of G, G \ e denotes edge deletion, and G / e denotes contraction. Tutte refers to such a function as a W-function. [1] The formula is sometimes referred to as the fundamental ...