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Elementary operations or editing operations, which are also known as graph edit operations, create a new graph from one initial one by a simple local change, such as addition or deletion of a vertex or of an edge, merging and splitting of vertices, edge contraction, etc.
Although such complex edit operators can be defined in terms of more elementary transformations, their use allows finer parameterization of the cost function when the operator is cheaper than the sum of its constituents. A deep analysis of the elementary graph edit operators is presented in [10] [11] [12]
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
A graph is called prime when it has no nontrivial splits. 3. Vertex splitting (sometimes called vertex cleaving) is an elementary graph operation that splits a vertex into two, where these two new vertices are adjacent to the vertices that the original vertex was adjacent to. The inverse of vertex splitting is vertex contraction.
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel.It was published in 1990 by Academic Press [1] [2] [3] with a revised edition in 1994 [4] and a paperback reprint of the revised edition by Dover Books in 2003. [5]
In computational linguistics and computer science, edit distance is a string metric, i.e. a way of quantifying how dissimilar two strings (e.g., words) are to one another, that is measured by counting the minimum number of operations required to transform one string into the other.
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.