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Multiple edges joining two vertices. In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or in a directed graph, two or more edges with both the same tail vertex and the same head vertex. A simple graph has no multiple edges and ...
A 1-forest, sometimes called a maximal pseudoforest, is a pseudoforest to which no more edges can be added without causing some component of the graph to contain multiple cycles. If a pseudoforest contains a tree as one of its components, it cannot be a 1-forest, for one can add either an edge connecting two vertices within that tree, forming a ...
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally independent graphs.
Multiple edges, not allowed under the definition above, are two or more edges with both the same tail and the same head. In one more general sense of the term allowing multiple edges, [5] a directed graph is an ordered triple = (,,) comprising: , a set of vertices (also called nodes or points);
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [1] [2] Such a drawing is called a plane graph, or a planar embedding of the graph.
Empty - has no edges. Non-simple (or multiple) - has loops (hyperedges with a single vertex) or repeated edges, which means there can be two or more edges containing the same set of vertices. Simple - has no loops and no repeated edges.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same ...