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In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. [1] Formally, given a graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph.
A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic.. In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.
The clique-width of a graph G is the minimum number of distinct labels needed to construct G by operations that create a labeled vertex, form the disjoint union of two labeled graphs, add an edge connecting all pairs of vertices with given labels, or relabel all vertices with a given label. The graphs of clique-width at most 2 are exactly the ...
In computer science terms, a property graph is a data structure representing entities associated by directed relationships, where the nodes and relations can both include multiple attributes / properties; In terms of graph theory, a property graph is a directed multigraph, whose vertices/nodes represent the entities of the corresponding data ...
The definitions of labeled multigraphs and labeled multidigraphs are similar, and we define only the latter ones here. Definition 1 : A labeled multidigraph is a labeled graph with labeled arcs. Formally: A labeled multidigraph G is a multigraph with labeled vertices and arcs.
In this approach, a formula in first-order logic (predicate calculus) is represented by a labeled graph. A linear notation, called the Conceptual Graph Interchange Format (CGIF), has been standardized in the ISO standard for common logic. The diagram above is an example of the display form for a conceptual graph.
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An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises , also called contention and reasons . [ 1 ]